Blockchain: Research and Applications 6 (2025) 100306 Contents lists available at ScienceDirect Blockchain: Research and Applications journal homepage: www.journals.elsevier.com/blockchain-research-and-applications Research Article Economic DAO governance: A contestable control approach Jeff Strnad StanfordLawSchool,Stanford94305,CA,USA A R T I C L E I N F O A B S T R A C T Keywords: In this article, we propose a new form of decentralized autonomous organization (DAO) governance that uses a Blockchain governance sequential auction mechanism to overcome the entrenched control issues that have emerged for DAOs by creating Decentralized autonomous organizations a regime of temporary contestable control. The mechanism avoids potential public choice problems inherent in DAO voting approaches but at the same time provides a vehicle that can enhance and secure value that inheres to DAO DAOgo vernance voting and other DAO non-market governance procedures. It is robust to empty voting and is code feasible. The Controlauction s mechanism not only facilitates the ability of DAOs to meet their normative and operational goals in the face of Cryptocurrencyregulation DAO regulation diverse regulatory approaches, but also strengthens the case for creating a less burdensome but at least equally Auction mechanisms effective regulatory regime for DAOs that employ the mechanism. Designed to shift control to the party with the Empty voting most promising business plan, at the same time, it deters value destruction by control parties, maximizes social surplus, and distributes that surplus in a way that tends to promote investment by other parties both at start up and on an ongoing basis. 1. Introduction Token voting potentially clashes with the goal of decentralization because of the danger of two types of entrenchment that threaten to Decentralized autonomous organizations (DAOs) are a recent inno- create the equivalent of centralized management. First, explicit contro l vation, dating from the April 2016 launch of “The DAO” [1]. DAOs is attainable by accumulating a sufficiently large token position. Second, operate largely through the execution of code and have no centralized it is often the case that a chronic lack of voter participation puts implicit management. When participant decisions are required, DAOs typically contro lin the hands of a small set of active token holders who regularly utilize voting by token holders, roughly analogous to shareholder voting engage in governance voting.3Chronic lack of participation is consistent in a corporate setting. In most cases, the tokens are publicly traded. with rationality in many instances. The passive token holders may be Governance issues for DAOs have received considerable attention of portfolio investors or may have a small enough holding that the costs late. Lots of experiments with governance are taking place, as is a large of being an informed voter greatly exceed the potential benefits in the volume of commentary.1Most of the experiments have centered around form of higher token values or otherwise, especially in light of the low different voting mechanisms, including quorum-based token voting, a probability of being the decisive voter with respect to each proposal. “direct democracy” approach in which token holders vote on proposals More generally, the benefits of any effort expended by a token holder subject to a quorum requirement, and approaches in which delegation to become an informed voter will accrue mostly to other token holders or other forms of representation are possible.2 who are in effect free riders.4 E-mail address :jeffstrnad5@gmail.com. 1 The Decentralization Research Center (formerly, the DAO Research Collective) website [2] includes a significant and representative collection of commentary and descriptions of experiments under the headings “Governance” and “Decentralization.” 2 See Nigam et al. [3](section on “Voting systems”) and Wandler [4]. 3 See, e.g., Feichtinger et al. [5], Fritsch et al. [6], Liu [7], and Sun et al. [8]. Feichtinger et al. [5, pp. 5–6, 8]documented very low Nakamoto coefficients, expressing the minimum number of token holders or delegates with more than half the voting rights, for a sample of 21 DAOs, including many of the most prominent ones. 17 of the 21 DAOs have either a delegate or token holder Nakamoto coefficient of less than 10. They also find very low participation rates for token holders. Liu [7]found similar levels of both concentrated control and low participation in a sample of 50 DAOs. Fritsch et al. [6]identified similar patterns for Uniswap and Compound in a more detailed examination of 3 DAOs. In a study focused on MakerDAO, Sun et al. [8, p. 26]found that “voters are centralized in a small group and voting power is unequally distributed among these voters. In most voting activities, the largest voters could account for a significant proportion of votes.” 4 Khanna [9, pp. 239–240]described this collective action problem in the corporate setting with reference to some of the literature. Reyes et al. [10, p. 26]appear to be the first to note the presence and importance of the same problem in the DAO setting. https://doi.org/10.1016/j.bcra.2025.100306 Received 24 November 2024; Received in revised form 3 May 2025; Accepted 4 May 2025 Available online 20 May 2025 2096-7209/© 2025 THE AUTHORS. Published by Elsevier B.V. on behalf of Zhejiang University Press. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/) . J.Strnad Blockchain: Research and Applications 6 (2025) 100306 In order to address the danger of entrenchment as well as several The mechanism described above defeats potential entrenchment in other major potential problems for DAOs, we propose a different ap- the form of explicit or implicit control. Holding a majority or super- proach to DAO governance centered on a sequential auction mechanism. majority of tokens no longer secures control of the DAO. The majority The fundamental building block of the mechanism is a basic auction that holder may lose control to a party with little or no token stake by be- grants the auction winner temporary, contestable contro lof the DAO. Bids ing outbid in a basic auction, and a basic auction may be initiated at in the basic auction consist of a token target price, a surplus claim, and any time by a party willing to submit an initial bid. Similarly, implicit revelation of any toehold position held by the bidder at the time of the control is insecure. A single challenging party can initiate an auction bid. Under the mechanism, the target token price part of the bid is effec- contest for control even in the presence of total passivity on the part tively a value claim, 𝑆, by the bidder that, with control, the bidder can of the vast majority of token holders, the passivity that enabled a small implement a business plan that increases the token value from the pre- group to control the DAO implicitly. vailing market price, 𝑃 , at the time of the bid to 𝑆. The surplus claim The social value properties of the mechanism emerge definitively 0 part of the bid is a claim by the bidder to a portion of the total added only if the token value of the DAO represents the intrinsic value of token value, (𝑆−𝑃 )𝑞, generated if the token target price is attained, the DAO itself. As a result, the proposed approach is limited to eco- 0 where 𝑞 is the total number of tokens outstanding. The winning bid is nomic DAOs, which are defined as DAOs with publicly traded governance the one that leaves the largest amount of added token value to the other tokens for which the token value reflects the inherent value of the en- token holders, that is, the bid that maximizes total added token value terprise. minus the sum of the bidder’s surplus claim and the expected gain on DAOs vary greatly in purpose and approach. Some DAOs are very the bidder’s toehold position if the value claim, 𝑆, is realized. similar to commercial businesses, providing services such as a trading In Section 4 and Appendix A.1, we show that the dominant strat- exchange. These commercial DAOs are the most obvious example of eco- egy in the basic auction is for the bidder to choose a business plan nomic DAOs. They provide goods and services with the profits accruing that produces the largest possible social surplus, (𝑉 −𝑃 )𝑞−𝐶, the total to token holders. The market capitalization of a commercial DAO rep- 0 added token value minus the bidder’s cost, and to truthfully reveal the resents its value in terms of the risk-adjusted present value of future token value, 𝑉, that the bidder envisions as attainable under that busi- returns. However, economic DAOs are a much broader category. All ness plan. As a result, with some minor exceptions, the mechanism will that is necessary is that the market capitalization represents the value choose the socially best project, the one that maximizes (𝑉 −𝑃 )𝑞−𝐶. of the enterprise to the token holders. A charitable or investment DAO, 0 In addition, because the winning bid is the one that allocates the largest for example, might gather funds to donate or invest. These DAOs might amount of social surplus to the existing token holders, the mechanism have particular objectives, such as promoting environmental or climate will tend to maximize the amount of such surplus realized by token change goals. Greater effectiveness at what they do in the view of all holders from future innovations, which in turn will tend to maximize potentia lparticipants, including the specification of the objectives them- the market value of the DAO both at start up and on an ongoing basis. selves, translates into a higher demand for the tokens along with higher The basic auction moves the DAO from a default governance state that market capitalization.5 typically is a voting regime into a control period in which the winning An important ideal for a DAO governance mechanism is for most, bidder controls the DAO independent of holding the majority or super- and ideally all, aspects to be code feasible. Code feasible means im- majority of tokens required to secure control under the voting regime. plementable using available blockchain technology without recourse to This feature allows the other token holders to enjoy a majority or even external institutions. Code feasibility is a key aspect of decentralization, an overwhelming majority of the social surplus generated by the win- close to a necessary condition. By decentralization, we mean the ability ning bidder’s project through their token ownership. Token ownership of the token project to operate in the absence of trusted parties. and control are separated during the control period. The desideratum of code feasibility distinguishes the case of DAOs The sequential aspect of the mechanism ensures that control arising from conventional corporate or public governance structures. Those from a basic auction is temporary. There are several terminating events. structures depend primarily on human management rather than code If the control party succeeds in reaching the token target price on a sus- implementations that are automatic and, at present, are also more con- tained basis, control ends and the DAO reverts to its default governance strained by various legal requirements and regulations. The mechanism state. The control period ends if there is a supervening auction and the developed here is potentially applicable to the governance of some con- control party fails to win that auction. Control is contestable because ventional institutions, in particular, public corporations. We leave full the mechanism allows a supervening auction to take place at any time, consideration of such applications to future work because they involve triggered by any party willing to make an initial bid. Finally, the con- their own considerable and distinct complexities as well as a different, trol period is limited in time and ends when the limit is reached, even more stringent set of legal constraints. On the other hand, theoretical if the token target price was not realized and there was no supervening work and experience with the governance of conventional institutions auction. are pertinent, and we draw on both in what follows. Section 4details a set of features that create appropriate bidding and The sequential auction mechanism proposed here eliminates the dan- project execution incentives for control parties. Control parties that fail ger of entrenchment inherent in token-voting schemes. It also has some to achieve the token target price forfeit a portion or all of a substantial very positive social value aspects: It tends to promote the choice and im- value deposit to the other token holders, guaranteeing that those token plementation of the best set of business plans while at the same time se- holders receive the full benefit of the winning bidder’s claimed future curing the highest possible initial and ongoing investment value for the performance, whether or not execution is successful. Value destruction DAO by allocating as much social surplus as possible to existing token occurs when parties in control of the DAO take damaging actions that reduce the value of the DAO. Value destruction is a serious concern with respect to the auction mechanism because control may be separated 5 Exit and entry through the token trading market is easy and nearly costless from ownership to an extreme degree. A winning bidder with control but for publicly-traded DAOs. The associated community is open, not limited to very few tokens can take a large financial short position and then tank current token holders. As a result, designing a governance system for a publicly the DAO in order to profit. The mechanism deters value destruction by t s r u a c d h e a d s D n A at O io n is s t v a e t r e y s o d r i ff so er c e ia n l t c f l r u o b m s th d a e t s i a g r n e i n re g l a s t u iv ch el y a c s lo ys s t e e d m b e f c o a r u c s o e m m m ov u i n n i g ti e in s the threat of potential loss of both the value deposit and an additional and out of the community voluntarily is much more costly or even impossible. surety deposit, which can be set large enough so that value destruction A range of non-commercial DAOs can be analogized to cities and towns offering is never profitable. The threat of losing the value deposit also creates different mixtures of local public goods in exchange for different packages of appropriate post-auction incentives for the control party to execute the taxes to residents and potential residents in a hypothetical world characterized business plan successfully. by negligible moving costs. 2 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 holders. Going further, it is important to consider how the mechanism is strikingly, (ii) a series of majority votes between two alternatives can related to voting approaches, decentralization, and the associated Web3 lead to any alternative in the choice space, even those that are Pareto ideals that emphasize the role that DAOs can play in creating new kinds dominated. Most DAOs operate through a sequence of such majority of democratic communities. Section 2addresses the interaction of the votes, and it is unlikely that the choice set of possible directions of mechanism with voting approaches, which is possible without first go- change consistently reduces to one dimension that fully captures pref- ing through a more technical description of the mechanism. This section erences. has an introductory aspect because the interaction with voting is one Most generally, there is the Gibbard–Satterthwaite Theorem derived motivation for the sequential aspects of the mechanism. Section 3pro- by Gibbard [13]and Satterthwaite [14]which states that if individual vides a conceptual overview of the mechanism with reference to the preference orderings are complete and transitive but otherwise unre- preexisting corporate governance literature. Section 4and the two ap- stricted and there are at least three alternatives, then a direct mechanism pendices present the full, technical version of the mechanism, including is dominant strategy incentive-compatible if and only if it is dictatorial.7 some evaluative aspects that arise naturally as part of the presentation. In a rough sense, what the theorem means is that with unrestricted Section 5contains further evaluation, including a subsection discussing preferences, a mechanism in which each individual votes sincerely, decentralization and closely related regulatory considerations. Section 6 recording their actual preferences, will work only if there is a single concludes with an assessment of the mechanism in light of Web3 ideals. individual who decides everything or if there are no more than two alter- natives. Once strategic voting enters the picture, the results can become 2. Interaction of the mechanism with voting unpredictable, difficult to estimate, and possibly very unrepresentative compared with voters’ actual preferences.8 The mechanism enables not only a sequence of auctions for con- The mechanism allows a way around these social choice problems. trol but also possible intervening periods in which governance reverts The basic auction creates a determinate outcome, one that awards con- to a default governance state, typically a voting method of some kind. trol to the party that claims it can perform in a way that has the most This approach allows the mechanism to achieve both operational goals benefit for the other token holders, a claim that is backed up by a value and procedural goals in any combination or sequence. As discussed deposit. Initiating an auction not only creates determinacy but is also previously, at the operational level, the basic auctions comprising the a way to address any inferior operational or procedural outcomes that sequence allow identification of the best business plans for the DAO, emerge from the social choice process. combined with a tendency to implement them in a way that shifts as Aside from the general social choice problems detailed above, there much social surplus as possible to existing token holders from the con- are risks associated with particular DAO voting methods. As documented trol parties who undertake the implementation. When no party is will- in Wandler [4], delegation is a common feature of DAO governance, ing to bid for control, the mechanism restores the default governance “used in some shape or form by nearly all large DAOs.” “Delegation” state. is commonly understood to mean transferring one’s voting rights to an- Aside from operational efficiency, DAO participants may value par- other voter rather than “abstaining,” not exercising one’s voting rights at ticular procedural approaches that embody process values in the form all. We follow this common understanding despite the fact that abstain- of certain community, “democratic,” or participatory norms. Potential ing is equivalent to delegating proportionately to active participants control periods allow for a reset of the default governance state when it based on the number of voting rights that they exercise [17–19]. We departs from the desired process values or, more ambitiously, revision define “direct participation” and “participating directly” as exercising of the default governance state itself. In terms of voting methods, the one’s voting rights directly, even though abstaining can be considered mechanism is available to preserve process values both by providing a participation in some sense, especially if it is considered and deliberate. guardrail that corrects voting method failures in an interim fashion be- We define “visible engagement” to mean delegation or direct participa- fore reinstating the method and by facilitating comprehensive reform of tion. the voting method itself if desired by current and potential DAO partic- One goal of delegation is to make visible engagement easier for vot- ipants. ers who do not want to participate directly, and the hope is that such Three subsections follow. The first two describe how the mecha- engagement will serve as a possible counter to the danger that voter pas- nism can correct possible voting method failures that may have negative sivity will lead to implicit control of the DAO by a small group of active operational or procedural consequences. The third addresses how the parties. Increasing direct participation is another possible route toward mechanism can promote process values. the same goal. However, there are potential problems arising from both delegation 2.1. Addressing social choice problems and increased direct participation. Most importantly, there is the danger that delegation or increased direct participation can reduce the likeli- At present, DAOs typically operate through a series of votes on pro- hood that the DAO will make good decisions. In addition, delegation can posals. If vote buying or other forms of bargaining with side payments lead to what Wandler [4]terms “recentralization,” the concentration of are not possible, then each voting approach, whether directly or through the bulk of voting rights in a few hands. electing representatives, can be conceptualized as a mechanism with Both problems are particularly evident in the case of liquid democ- nontransferable utility.6 As such, a large series of well-known poten- racy, a form of delegation that allows voters to change their delega- tial “social choice” pathologies arise. A striking and relevant instance is tions at any time or to withdraw them and participate directly. Multiple the McKelvey-Schofield Chaos Theorem derived by McKelvey [11]and rounds of delegation and redelegation can occur before a vote. Theoret- Schofield [12]. This theorem states that if the choice space is more than ical studies by researchers such as Kahng et al. [20]and Bloembergen one-dimensional and preferences are Euclidean (decline with distance et al. [21]suggested that liquid democracy under at least some plausi- from an ideal point) or, more generally, are convex as delineated in ble assumptions can lead to a concentration of voting power that also Schofield [12], then (i) majority voting is unstable in the sense that ev- reduces the probability of correct decisions because the independent in- ery alternative is dominated by at least one other alternative and, most formation of other voters is lost. In the study by Mooers et al. [19], this 6 Nontransferable utility implies that players cannot bargain with each other 7 Borgers [15]provided a concise discussion and proof of this theorem and its using money or some similar indicator of value to reach a mutually agreeable significance. result. Pareto improving moves, where, for instance, party A buys off party B to 8 The discussion by Tabarrok and Spector [16]about how strategic voting achieve a particular outcome that results in gains for A that outweigh the losses might have affected the U.S. Presidential election of 1860 under various voting for B are not possible. regimes is a good example. 3 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 result emerges in an experimental setting despite the use of a framework Empty voting exists in conventional markets and has been docu- in which theory suggests that liquid democracy will produce superior mented by Hu and Black [23] as well as in a substantial literature outcomes to majority voting. Voters overdelegate, their voting power following them. There are also identifiable instances of empty voting becomes concentrated, and liquid democracy underperforms majority in cryptocurrency markets, along with an awareness of the possible use voting. Empirical studies are not encouraging either. In an impressive of empty voting among participants in those markets.12Commentators, empirical analysis of liquid democracy in practice spanning 250,000 including Hu and Black [23], consistently point out that empty voting votes and 1,700 proposals across 18 DAOs, Hall and Miyazaki [22, p. 3] can have positive as well as negative effects. Brav and Mathews [26], for found that “delegation is somewhat lumpy, leading some delegates to instance, modeled whether empty voting is likely to have a net positive amass considerable voting power, consistent with theoretical concerns or negative effect on corporate governance. about overdelegation.” Whatever the balance between the positive and negative effects, More generally, the impact of delegation and increased direct par- empty voting creates an element of arbitrariness because prevailing may ticipation on the likelihood of making good collective decisions is very be a matter of more effectively accumulating empty votes rather than uncertain. Substantial negative impacts are possible and, in some situa- the result of being able to create more value or virtue.13 tions, quite plausible. Strnad [18]showed that regardless of the number In the context of a battle for control, the mechanism developed here of steps, an unrealistic degree of information is required for a single makes empty voting irrelevant, avoiding any possible accompanying ar- voter to be able to delegate in a way that is assured to increase rather bitrariness. Any party can initiate an auction, and to win control, a party than diminish the probability of DAOs making correct decisions even must submit the best bid, one that promises an outcome that delivers assuming the voter can “move last” after learning the delegation deci- the largest possible social surplus to the other token holders, with a sions of all other voters. On the direct participation front, Strnad [18] guarantee in the form of a value deposit. It does not matter how many showed that adding direct participants is only guaranteed to increase conventional token votes the party or its competitors have, empty or the probity of decisions under very special conditions and that a sub- otherwise. stantial degradation of DAO decision-making quality can result under Empty voting can facilitate value destruction. A party can take a circumstances that easily arise in practice.9 large empty voting position, combine that position with a net nega- None of these considerations means that delegation and increasing tive economic interest in the token, such as a collection of put options, direct participation are valueless. As noted in Wandler [4], DAO gov- and then vote for proposals that reduce token value.14 In the most ex- ernance is a very active area of experimentation. It may be that some treme case, the party could promote governance decisions that totally strong methods will emerge based on delegation or increasing direct par- destroy the value of the token and the DAO project. The mechanism pro- ticipation. However, what is true is that current approaches are risky in posed here creates potential protection against such value destruction terms of DAO performance, and in view of the difficulties encountered strategies because it offers a profitable auction route that renders empty so far, as well as the general social choice results we started with in this voting ineffective. subsection, some of that risk may be irreducible. The mechanism itself implicitly relies on empty voting because it That is where the mechanism comes in. If a DAO begins to perform permits a party winning control to prevail in all votes during the ensuing poorly because some of the governance risks are realized, the mecha- control period, despite falling short of holding the required majority of nism allows for a corrective reset, combined with selecting the best way tokens. As a consequence, potential value destruction by the control forward from a performance standpoint. party is a concern. As discussed in Section 1and described in detail in Section 4, the mechanism contains measures to deter value destruction 2.2. Addressing empty voting by a control party regardless of how it arises. Value destruction triggers a potential loss of deposits that outweighs any potential benefits and In addition to the social choice difficulties with voting approaches, that compensates existing token holders for any resulting drop in token there is another entirely separate set of potential problems associated value. with what has been termed “empty voting.” Following the seminal work Designing the mechanism involves considering the possible delete- of Hu and Black [23], we use the following terminology. Empty voting rious use of hidden ownership as well as empty voting. In particular, occurs when a party is able to exercise the voting rights of a token with- Section 4.1.4describes the need for accurate toehold reporting accom- out holding the associated economic rights to token value appreciation panying auction bids. Hidden ownership is one way to conceal part or and any distributions. Hidden ownership is the opposite: The party holds all of the bidder’s token position, and the mechanism must defeat the the economic rights without the right to vote the token and, typically, use of such a device, even if it is hard or impossible to detect as such. without appearing to be an owner in any corporate or blockchain regis- ter. at all, but the party still formally owns the token and can vote it. The cost of Empty votes can easily be created at little or no cost by a variety entering this position will be nominal except possibly for some fees, which will of means. A party can borrow tokens and then vote them, leaving the be low if there are active markets or if potentially competing over-the-counter economic ownership to the lender. A party can engage in an equity counterparties are readily available. swap, offloading the economic rights and retaining the votes.10 There 12 Buterin [24]discussed “vote buying” and presents a theoretical example of are many methods that employ derivatives.11 empty voting that consists of the equivalent of an equity swap. Copeland [25] described an actual example from the takeover of Steem in 2020 by Justin Sun. 13 As Hu and Black [23, p. 907]stated in the corporate context, potential use 9 For example, adding large groups of direct participants who have the same of empty voting leads to a situation in which: information set or who are only a little better than chance at making correct decisions can cause precipitous drops in the quality of the DAO governance Voting outcomes might be decided by hidden warfare among company in- mechanism in terms of the probability of making correct decisions. siders and major investors, each employing financial technology to acquire 10 For example, the party starts with some tokens, then swaps the economic votes. Adroitness in such financial technology may increasingly supplant the return from the tokens for the economic returns of, say, a Treasury bond of role of merit in determining the control of corporations. equal value. The party still holds the tokens and can vote them, but the economic interest is in the hands of the swap counterparty. 14 There may be other motives to destroy the token, such as being a market- 11 For example, the party holding a token can write a call, buy a put, and place competitor. Hu and Hamermesh [27]discussed a general class of “related borrow from a counterparty. The short call removes the token upside, the long non-host assets” situations where an investor might use empty votes to damage put eliminates the downside, and the party can lend out the cash to pay the the value of one entity in order to enhance the value of another entity in which interest on the amount borrowed. The party is left with no economic position the investor holds a substantial equity stake. 4

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 More generally, it is important for any DAO governance approach innovation in the default governance state through voting or other pro- or mechanism to be EV-robust in the sense of being effectively resistant cedures that comprise the current state. both to deleterious uses of empty voting or hidden ownership and to any Third, the fact that process value is reflected in token value means tendency for the decision mechanism to be compromised or blurred as a that a DAO that has sacrificed operational efficiency to add an even result of either manipulation.15This task is complicated by the fact that larger amount of process value will be immune from a takeover through empty voting and hidden ownership are easy to conceal, particularly the auction mechanism that eliminates the process value to increase op- because the elements that result in empty voting or hidden ownership erational efficiency. A party intending to implement this move through positions may otherwise have legitimate hedging or other purposes. The an auction would be unable to initiate the auction if the DAO is cur- mechanism will not be EV-robust unless it is impervious to concealed rently fully valued and would lose in the auction if the DAO is currently empty voting or hidden ownership. undervalued.18 2.3. Promoting process values 3. Conceptual overview We assume that the subject DAO is an economic DAO. We consider a Although voting approaches have serious potential flaws, voting setting similar to Burkart and Lee [29]in which various parties can use mechanisms and other governance elements may have a process value costly effort to increase the value of the DAO. In particular, suppose that to participants independent of operational efficiency. One would expect each party can engage in various projects that involve expending effort, that process value would be captured in token value because token hold- labor, and resources equivalent to 𝐶monetary units, in order to increase ers will be willing to pay more to participate in a DAO with governance the value of the DAO by 𝑁(𝐶)monetary units.19Suppose that the DAO features they value. Three implications follow with respect to the auc- has 𝑞 tokens outstanding and that the current market price per token tion mechanism. is 𝑃 . Define 𝑉 =𝑉(𝐶)=𝑁(𝐶)∕𝑞+𝑃 to be the token value emerging 0 0 First, there is rescue. If the indeterminacies and potential pathologies from a particular business plan. This business plan will create social sur- of voting threaten the coherence or direction of the DAO during an open plus, 𝜓=𝑁(𝐶)−𝐶=(𝑉 −𝑃 )𝑞−𝐶. Consider that expectations about 0 period, causing the value of the DAO to drop, an auction that initiates the nature of future value-additive projects and about the distribution a control period is a remedy. The control party can set the DAO back of social surplus from those projects will affect the initial funding value on course during the control period and then reinstate the voting mech- of the DAO, possibly being critical to having enough funding to start up anism after addressing the threats. This feature may create a safe zone at all. In other words, the expected later treatment and facilitation of of operation for voting mechanisms that serve important participation value-added projects will have an investment impact on initial funding or other normative goals despite their potential flaws.16Otherwise, the for DAOs, and also, in an obvious way, on the ongoing investment value voting mechanism may not be viable as a long-term way to operate the of the DAO, which continues to depend on possible future projects. DAO. The target is the following first-best outcome: Second, the auction mechanism is a means to promote process val- ues, including various desired voting approaches, by facilitating inno- A) At any point after the initiation of the DAO, the mechanism will fa- vations in the default governance state. If an increase in token value is cilitate the implementation of the value-additive project that results attainable by shifting the governance mechanism in a way that increases in the highest social surplus 𝜓. its process value without a fully offsetting loss in operational efficiency, B) When such a project is created and implemented, the mechanism then there is potential for an auction to create the shift. The sequen- will allow the creating party to cover its cost but will allocate the tial aspect of the auction mechanism is designed to achieve this result. social surplus entirely to the other token holders. Successful implementation of a shift in the default governance mecha- nism after winning an auction will raise token value, ending the control If both targets are met, the result will be the highest positive investment period with a reversion to the new superior default governance mecha- impact as initial and ongoing investors will receive the maximum possi- nism.17It may be difficult or impossible to achieve a possibly complex ble benefit from future innovations.20In addition, at each point in time, the DAO will implement the ongoing business plan that adds the highest possible amount of social surplus. 15 The term “EV-robust” uses the initials “EV” to stand for “empty voting.” To aim at the target, we create a sequential auction mechanism that Whenever hidden ownership is created, it is necessarily the case that there will produces periods of temporary contestable control interspersed with be an offsetting empty voting position. Thus, “EV-robust” is an appropriate de- periods in which the DAO reverts to a default governance state. The scriptor that can refer to the hidden ownership side of the pairing as well as to empty voting itself. 16 Hall [28]described elegantly how the history of democracy could inform 18 Initiating an auction requires a bid with a token target price in excess of the design of DAOs. Among other elements, he considers the various forms the current token value. If the DAO is undervalued but the current operational that delegation can take, including delegates of the token holders appointing efficiency plus governance mechanism maximize the total value of the DAO, “managers ... who could take certain operational decisions more expertly than then a bidder maintaining the status quo will win the auction. See Section 4for tokenholder voting could,” but who remain “accountable to tokenholders be- details. cause they can be fired by the elected delegates at any time.” He notes that this 19 These costs are external to the DAO and are borne by the party engaging approach bears “similarities to corporate governance.” The mechanism here can in the project. If the party uses DAO resources such as DAO treasury assets to be seen as an extension that adds a way to right the ship through temporary, execute the project, use of these resources will diminish the value of the DAO contestable delegation of control to a competent party if the usual voting and directly, reducing 𝑁(𝐶)rather than being an addition to 𝐶. delegation mechanisms break down. It is analogous to external corporate gov- 20 Posner and Weyl [30]envisioned a system of “partial common ownership” ernance through the market for corporate control. in which there were property taxes and contestable control, at least periodically, 17 The ideal situation is one in which the winning bidder sets the token tar- for various kinds of property through a Harberger tax mechanism. Central to a get price just high enough to fully reflect the increase in token value from the Harberger tax is a method of assessment aimed at eliciting the owner’s actual shift in default governance mechanism. Execution results in a rapid, if not in- valuation. The owner states a value that will be the basis for imposing a prop- stantaneous, increase in token value to the target level, which ends the control erty tax, but understatement is policed by the right of the state or others to buy period. If the winning bidder sets the token target price too low, then the same the property at the claimed value. In the case of multiple potential buyers, some- result occurs. If the winning bidder sets the token target price too high, then, as thing like the mechanism here is required to allocate the property to the buyer discussed in Section 4, the existing token holders will enjoy any overage at the who can produce the highest possible social surplus, the owner’s valuation being expense of the winning bidder. equivalent to 𝑃 in the model here. 0 5 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 mechanism has the property that the highest social surplus project is token value on the retained proportion that is not purchased by the cre- chosen, subject to some constraints that guarantee the continuation of ator. This feature makes the auction equivalent to a merger in which market trading. Some social surplus necessarily leaks to the project cre- token holders receive only a portion of the expected total added token ators, resulting in an outcome that falls short of the first best. value on their token position shares because of the terms of the merger To describe the setting further, we use some terminology from which dictate the proportional stake in the merged entity that they re- Burkart and Lee [29]: Jensen-Meckling free riders and Grossman-Hart free ceive in exchange for their shares in one of the precursor entities.23The riders.21Jensen and Meckling [31]pointed out that when the party man- bidding mechanism creates an incentive for bidders to limit the amount aging a corporation expends all the effort but owns less than all of the of total added token value that they attempt to claim via the freeze- common stock, the costly effort is matched with only part of the gains. out feature to the lowest possible value, the amount required to cover The other shareholders are Jensen-Meckling free riders, reaping gains their costs while taking into account the expected gain in their toehold without bearing any of the costs. These free riders, however, are the position. As discussed in the next section, there typically will be some successors of the original investors or of parties who contributed effort leakage because the winning bidder will have some scope to go beyond previously. A policy of rewarding them encourages initial or subsequent that limit. investments in the corporate project, having the investment impact de- Second, there is the problem of post-auction incentives in the face scribed above. of Jensen-Meckling free riding. At the end of the auction, the winning The conventional picture of Grossman-Hart free riders is a corporate bidder has control but owns less than all of the tokens. The auction enterprise for which the equity holders consist of a large group of par- mechanism is designed to allocate social surplus to the other token hold- ties, all of whom own a very small stake. The chance that any one such ers by limiting the stake held by the winning bidder, and that stake may party will be decisive in a vote is minuscule, which, combined with the be much less than half of the outstanding tokens. The mechanism re- large number of holders, creates a collective action problem. Consider stores full incentives to execute through the value deposit described in a project creator who can profit by building up a share ownership posi- tion and then announcing or implementing a project that increases the Section 1and discussed more fully below. To the extent that a control value of the equity. If the equity holders get wind of the project, they party falls short of the target price, they have to cover the shortfall for will free ride by refusing to sell at less than the post-project target value all of the other token holders in addition to losing out on their own to- of the equity. Open market purchases by the creator will push the price ken position in the DAO. As a result, they have an incentive to execute up, and in the United States, the creator will have to reveal its holdings that is at least as large as a party that has 100% ownership, eliminating and intentions once the holdings exceed 5% of the total equity. Free rid- any adverse Jensen-Meckling impact on post-auction execution incen- ing by the equity holders will limit the portion of the total added token tives.24 value that the project creator can extract, potentially killing the project As discussed in Section 4.1.1, the value deposit and also the surety if the extractable portion of the total added token value is lower than deposit employed by the mechanism are equivalent to forcing the con- the creator’s costs. Alternatively, creators will pick projects that do not trol party to take on option positions. Other researchers, most promi- maximize social surplus but are viable based on the increase in market nently, Burkart and Lee [33], have described the strong potential role value available from a modest toehold. of requiring such positions in implementing a cogent market for corpo- Burkart and Lee [29]created a model based on the value impact of rate control.25 We use deposits rather than requiring option positions effort that captures the current situation for project initiation through because deposits are code feasible, while derivatives require counter- activism and tender offers in the United States. The tender offer route is parties, which raises issues of trust. restricted by Grossman-Hart free riding after an offer is made, limiting The approach here flows from a very general deposit-based model. the offeror to the added token value from a toehold. Activists proceed There is a single auction deposit, 𝐷 𝑎, and a deposit forfeit function, through a costly campaign aimed at managers and other shareholders to Φ(𝐷 𝑎 ,𝑃 0 ,𝑆,𝑋), where 𝑃 0 is the token price when the auction is initi- initiate a new project, avoiding Grossman-Hart free riding, but still be- ated, 𝑆 is the value per token that the winning bidder claims is attain- ing subject to Jensen-Meckling free riders. Revenues from activism are able, and 𝑋is an outcome, typically the token price when the winning again limited to a toehold, but the other shareholders potentially benefit bidder’s control terminates. The first three parameters in the function from the activism without bearing any costs. Burkart and Lee [29]also are set by the time the auction ends and the winning bidder takes con- analyzed a third route: activism directed at initiating a merger, which trol. The deposit forfeit function specifies the amount of the deposit that they term “takeover activism.” In a merger, the price that shareholders is forfeited for each possible value of 𝑋given the three auction parame- receive is set by the managers of the two firms, allowing additional total ters. The function is not required to be continuous in 𝑋, and we will see added token value to be made available by forcing the dispersed share- that discontinuities can play an important role in creating incentives for holders to accept a price below the target price.22Burkart and Lee [29] control parties. surveyed the empirical evidence and noted that among activist projects, the high-return projects for shareholders are concentrated among in- stances of takeover activism. The mechanism created here addresses the potential value-reducing 23 Although the mechanism creates an outcome somewhat analogous to a merger, no actual merger is involved. Trading in the DAO remains continuous, free-riding of both types through two devices. First, by creating a and the life of the DAO goes forward. A merger in which the acquiring party freeze-out feature as part of an auction, the mechanism addresses the buys all of the DAO shares would mean the end of the DAO in its current form. Grossman-Hart free rider problem by allowing the project creator to It might be that the acquiring party, which may be a shell, is itself set up to buy a proportion of the other token holders’ positions for no premium. be a DAO, perhaps one with a new set of smart contracts meant to upgrade the Those token holders will earn the full amount of the expected total added acquired DAO. We leave exploration of this possibility to future work, includ- ing the case in which the selling token holders receive tokens in the new DAO instead of a cash-equivalent in exchange for the tokens in the old DAO. 21 The names derive from phenomena described in Jensen and Meckling [31] 24 Complexities arise if control parties hedge part or all of their token position. and Grossman and Hart [32]. Section 5.4discusses this possibility and potential responsive adjustments to the 22 Most states require shareholders to approve a merger by a vote. It will be value deposit and the function specifying value deposit forfeit amounts. in the interest of shareholders to do so despite not receiving the target price 25 Burkart and Lee [33]showed that a signaling equilibrium in a setting in if a lower price is necessary to make the merger work by providing enough which there are private benefits to control can attain the full information out- surplus for the acquiring party, here, the project creator. Grossman-Hart free come by combining a cash offer with an offer to sell a call option with an exercise riding otherwise creates a collective action problem that potentially precludes price equal to the bid price. Here, the required option positions implicit in the shareholder gains entirely. deposits serve multiple roles, including one related to signaling. 6 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 Instead of operating at the level of full generality by choosing the From this point on, we assume for convenience that the total num- deposit amount and the deposit forfeit function to optimize some set of ber of tokens remains at 𝑞. Then token price differences translate linearly objectives, we consider a more limited version that employs two deposits into total value differences through the multiplicative factor 𝑞, even if and certain restrictions on the deposit forfeit function. This approach al- the prices are realized at different times. This assumption avoids hav- lows us to illustrate the features of the auction mechanism more clearly. ing to continually correct for possible changes in the number of tokens We leave a more general treatment to future work. outstanding, which is trivial but cumbersome. The goal throughout is to create an example of a mechanism that has A central feature of the basic auction is a freeze-out element which some plausibility and likely effectiveness in order to introduce the idea allows the winning bidder to force the other holders as of time 𝑇 to 1 of auction-based temporary contested control for governing DAOs. No sell 𝑡 𝑓 𝑞 of their tokens to the bidder at price 𝑃 0 . The main function of c m la e i c m ha i n s i m sm a s d . e W th e a d t i t s h c e u s m s e p c o h s a s n ib is l m e a i l s t e o r p n t a im tiv a e l a fe m a o tu n r g e s th a e t s m et a o n f y a p ll o s i u n c ts h , t t h h e e s v u a r lu p e lu s c la cl i a m im 𝑆 𝑅 en i d s s t o u p d e b t e e i r n m g i n c e o r 𝑡 r 𝑓 e , c t i , n t h p e a n rt i t c h u e l a f r o , r 𝑡 c 𝑓 e 𝑞 d = sal ( e 𝑆 − 𝑅 r 𝑃 e 0 s ) u . lt I s f n s e c p u u o v o o a p n a t s t i W t l e t o u - a a r a n t a i i i u t o n t t e o h c e r s m f t t i o i t t t h o p r h h i i n t e n r s i i n e n o o m t e f g h p v e e e e e r s t c i r r u o n o h a v b e r a t i c s x e i n t o o e t w o i c m n s t t w m t , i i e h n o a o . e n n t h S s o s d m a e e , n c c a s a d t t u d i i i c n e b , o o o s w s n n v c n e s r a e 5 q c , i r l b u a p c i u a l i e r o s o n n e n m i n g s o t t e g p n a t n r h l w u e e t c a s c t i o t t p e t t h n h i s e w o e c c t t n e e h w t m s i r e d v , n o e e e a t i c a a n l s l h y p o c s g a , k r p n n i w e g b a o i n s e f h w m d s . e e i i i v n t t c f h h a g e o e l s l r u s e r . m o a S m t t a a e h i u l c o e e l t c n y y i e t o i a v a a o n n n a r n l d d 4 e - , i t f b t o n r o o r i e d t e p a a t d z h l u e e t e r h - r r c o a o b h w u n l i a d t d s i s l i f d p l n e e r e r g o o o r s ff p , o f o o e f t t o r h r f g t k e i t a | o e h 𝑡 i n 𝑓 b n e n | . a s b 𝑞 , s e 𝑅 i i t q s d t h u o < d e f a k o e b l e 0 r r n i , t d t o i s i s h d . e a e 𝑅 e p . t r , o t = 𝑃 h e | s 𝑡 r s o 0 𝑓 m i 𝑡 l b 𝑓 | d t i o l ( ≤ s n e 𝑆 , o t t 𝑡 h h l 𝑏 − i o e n e . g A 𝑃 p o y w r 0 t t o ) h h “ t 𝑞 p h e i s c u o r e f h r r r h e p t o i c o n l m o a u l d n d s s e t e o 𝑡 h c r 𝑑 f 𝑡 l s e a 𝑓 t = h s i o m u < e 𝑡 t 𝑓 b h , f 0 ” j e o + e , r r 𝑡 c 𝑡 c 𝑓 a t h 𝑏 e n o t d o i d o s l f d s t t t t a e h h h h r le e e e e s total tokens, and all of these tokens must be deposited in the applicable is organized topically in separate subsections. One appendix consists of smart contract, resulting in the token deposit at the end of the auction p st r o o c o h f a s. s t T ic h e e l o e t m he e r n t a s p t p o e n th d e ix m e o x d p e lo l r d e e s v t e h l e o p c e o d n s i e n q t u h e e n c te e x s t o . f adding certain totaling 𝑡 𝑑 𝑞.27 The intuition behind the auction parameter, which will emerge with a more rigorous meaning in the propositions below, is as follows. 𝑆rep- 4. A sequential auction mechanism resents a claim by the bidder that the project will reach value 𝑆𝑞after tion W s, e i m co p n le s m tru en ct t e a d s v eq ia u e o n n ti e a l o a r u m ct o io r n e c s o m n a s r is t ti c n o g n t o r f a c a t s s , e r c i o e l s l e o c f t i b v a e s l i y c “ a t u h c e - t t 𝑅 h io e = n b ( o i 1 d f − d th e 𝑡 e r 𝑏 g − to a t 𝑡 i a 𝑓 n l ) s ( a c 𝑆 d o d n − e t d 𝑃 r o 0 to l ) . 𝑞 k T e = h n e ( v 1 a a u − lu c e 𝑡 t 𝑑 , i o ) ( ( 𝑆 n 𝑆 p − − a 𝑃 r 𝑃 a 0 m ) ) 𝑞 𝑞 e , , t t e w h r a h i t s i c t 𝐴 h h e = i s b ( p i 1 d r − d ec e 𝑡 i r 𝑏 s ) e w ( l 𝑆 y il l − t h d 𝑃 e e 0 l p i ) v 𝑞 o e − r r - DAO Code.” The DAO Code enables the DAO to operate through peri- to the other token holders if 𝑆, the bidd 0 er’s value claim, is realized. If odic basic auctions, with a fixed control period between auctions, subject the token value does not reach 𝑆, then, as discussed below, transfer of to early termination under some circumstances. The DAO Code also per- part or all of the value deposit to the other token holders will ensure mits a basic auction to be initiated by any party at any time, independent that they are at least as well off as if the value 𝑆 was realized. These of the periodic auctions. These features make the control created by the other token holders will receive at least their promised portion of the auction both temporary and continuously contestable. total added token value, whether or not the winning bidder successfully We develop the sequential auction mechanism in a deterministic set- executes the project.28 t o p i f l n a g t n h s i e . n I p w n r o h A g i p c r p h es e t s n h d a e i n x t d o A k p . e 2 r n o , s w p p r e e i c c c t e o s m n o s f o i d v e e e x r s i s w o ti n h n l a g y t a b m n a d i s g e h p d t o o t h e n a n p m t p ia a e l r n k f u e in t t u a a r s e s s t e b o s u c sm h si a n e s n e t s i t c s s con T d h it e io D n A g O u a C r o a d n e te i e m s p th o a se t s a a m m i a n r i k m e u t m siz p e r c o o p n o d r it t i i o o n n , 1 𝑡 𝑑 − = 𝑡 𝑚 𝑡 𝑓 o + f 𝑡 t 𝑏 he ≤ t 𝑡 o 𝑚 t . a T l h to is - kens remain in the market during and at the end of the auction, which setting, examining possible adjustments to the mechanism and possible may be necessary to ensure a functioning market after the auction is hedging by winning auction bidders.26 over.29Choosing any 𝑡 𝑚 <1limits the portion of the total added token value that can be shifted to the winning bidder to an amount less than 4.1. The basic auction the total added token value available.30 If the bidder has high enough 4.1.1. The basic auction mechanism A basic auction is initiated at a time 𝑇 0 by a first bidder making a 27 The bidder is not barred from buying tokens during the auction, that is, bid. The basic auction is open for the competitive bidding process up between time 𝑇 and time 𝑇 . Any such token purchases do not need to be until a winner is determined at some later time 𝑇 1 , with the fixed total reported or adde 0 d to the toke 1 n deposit. It is likely, and we are assuming, that time length 𝑇 auction =𝑇 1 −𝑇 0 of the bidding period specified in advance any such buying after the announcement of the bid will be futile both during by the DAO Code. Suppose that at time 𝑇 0 , the price of the DAO gov- the auction period and afterwards because Grossman-Hart free-riding effects as ernance token is 𝑃 0 , and 𝑞tokens are outstanding. A bid, 𝛽=(𝑆,𝑅,𝑡 𝑏), well as market maker reactions will defeat the bidder’s attempt to secure more consists of three parameters: a value claim, 𝑆≥𝑃 0 , per token; 𝑡 𝑏, the of the potential added token value. The toehold position is discussed further in proportion of the 𝑞tokens held by the bidder at 𝑇 , hereinafter termed Sections 4.1.4and 4.1.5infra. the bidder’s toehold or more simply toehold where 0 the context is clear; 28 This feature is an important aspect of the attempt to maximize the invest- a b su n y r d i t n h a g e s a D u d r A p e O l q u u s C a c o t l e d a i e m m t a , h r 𝑅 a k t e , ≤ t a l ( s i 𝑡 q 𝑚 d u i i − s d c i 𝑡 u t 𝑏 y s ) s . ( e 𝑆 T d h − e in 𝑃 b S 0 id e )𝑞 d c , t e i w r o ’ n s h t e 4 o r . e e 1 h . 𝑡 6 o 𝑚 , l d i p s , l 𝑡 a a 𝑏 y 𝑞 p s , a a i r s a r d m o e l e e p t o e in s r i t a s e e s d t - m t a If o l t e k t e h n e r e n t n a i w h m t o i i v n p ld e n a e c i b n r t u s g o s a f i b n r i t e d e h s d l e s i e k p r m e l m l a e y n c a h t s k o a e w n s b o i e s a u m n J ld e e d n x n e s c o e s e t p n s i b - s t M i e e v e e r t c a h v k t e i a l o i l f n u n a g e a c l t f c , r l t g e a h i e i a v m t e r i n m d t h e t o a h r s s t e t r f s o e o i s f r z u e t w l h t o s h e f o i n t n m h o e t n h a i - r e s b s s i d e t d a s e d s k f i i e e n n a s g g t . into the applicable smart contract simultaneously with the bid, becom- of a more capable bidder in the auction, the non-bidding token holders are pro- ing part of the bidder’s required token deposit under the mechanism. The tected automatically at the expense of the winning bidder who failed to perform basic auction is an English auction, ascending in the auction parameter, as claimed. 𝐴=(1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞−𝑅. All prices and quantities such as 𝑆, 𝑃 0 , and𝑅 29 The freeze-out step is proportional, leaving each holder immediately after are denominated in the units of a particular reference fiat currency des- the auction ends with the proportion 1−𝑡𝑓−𝑡𝑏 of their time 𝑇 holdings, i.e., the ignated by the DAO Code. same time 𝑇 market participants have h 1 o − l 𝑡 d 𝑏 ings, albeit propo 1 rtionately reduced. 1 This feature should allow the market to continue to function smoothly across the transition point. 26 The stochastic elements discussed in Appendix A.2include sources of value 30 Under the mechanism, 𝑡 𝑚 is the maximum proportion of tokens that the fluctuations, such as the impact of broader market movements on the DAO token control party can hold as part of the token deposit, leaving the rest to be freely value, that are not necessarily related to the cogency of business plans or the traded, i.e., 𝑡 𝑑 ≤𝑡 𝑚. The subscript 𝑚is chosen to signify “maximum,” while the quality of plan execution. subscript 𝑑signifies “deposit.” 7

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 costs, this limitation may cause a surplus-producing business plan not We stated the value deposit as an inequality above, 𝐷 𝑣 >(1− to be viable under the mechanism. 𝑡 𝑑)(𝑆−𝑃 0 )𝑞, rather than as a specific amount. Because the value de- In addition to the token deposit of the 𝑡 𝑑 𝑞 tokens, the bidder is re- posit plays multiple roles, it is valuable to leave flexibility because the quired to make three additional deposits in the form of stablecoins of optimal amount of the value deposit, along with the best accompanying types permissible under the DAO Code, representing units of the refer- value deposit forfeit function, may be application-specific. We have al- ence fiat currency: ready mentioned a role that is satisfied by a value deposit close to the (1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞bound: guaranteeing the transfer of the amount of gain 1) A value deposit: 𝐷 𝑣 >(1−𝑡 𝑑)({ 𝑆−𝑃 0 )𝑞. } that the winning bidder has promised to token holders other than the 2) A purchase deposit: 𝐷 𝑝=ma { x 𝑆− 𝑅 𝑃 0 𝑃 0 ,0 . } b am id o d u e n r, t w of h i s c o h c i h al e l s p u s r p a l t u ta s i t n o t t h h e e s g e o a o l t h o e f r s t h o i k ft e i n n g h o th ld e e m rs. a x H im ow u e m v e p r o , s o s t i h b e le r 3) A surety deposit: 𝐷 𝑠=max (1−𝛾)𝑃 0 𝑞−𝐷 𝑣 ,0 , where 𝛾 is defined considerations, several of which we discuss in ensuing subsections, sug- and discussed below. gest that a value deposit significantly larger than the bound may be useful. The bidder is making a value claim, 𝑆, that the bidder’s business plan The reason there is that a lower bound, and, in particular, the stated for the DAO will suffice to increase its value to at least 𝑆𝑞. The DAO one, relates to another role of the value deposit: ensuring that the bid- Code may refund part or all of the value deposit when the bidder’s con- ding mechanism works successfully. One goal of the mechanism is to trol comes to an end, with the rest forfeited and paid to the other token induce the bidder to make a value claim equal to the bidder’s honest holders. A value deposit forfeit function, 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 ref ), specifies for assessment of the token value attainable under the envisioned busi- each value of a reference price, 𝑃 , the value deposit forfeit amount given ref ness plan. Consider the following Lemma and Corollary of the Lemma, the three auction parameters 𝐷 𝑣, 𝑃 0 , and 𝑆. The amount of the value de- proven in Appendix A.1. The context is a bidder who makes a value posit that is refunded is 𝐷 𝑣−𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 ref ). When the control period claim of 𝑆and faces cost 𝐶to implement a business plan that the bidder is not followed immediately by a subsequent auction, the value deposit believes will increase the token value to 𝑉 from the price 𝑃 prevailing forfeit amount is precisely 𝜙. In this situation, as discussed below, the 0 at the initiation of the auction. forfeited amount is transferred to the token holders of record other than the winning bidder as of the end of the auction. Consider a standard case of a value deposit, reference price, and value Lemma 1. Given a business plan (𝑉,𝐶), a bidder will avoid making a deposit forfeit function defined by: value claim 𝑆>𝑉 if and only if for every possible outcome 𝑋∈[𝑃 0 ,𝑆], 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 𝑟𝑒𝑓 =𝑋)>(1−𝑡 𝑑)(𝑆−𝑋)𝑞 under the value deposit forfeit 1. 𝐷 𝑣=(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞(1+𝜖), where 𝜖>0is small or infinitesimal, function. creating only a slight deviation from 1. 2. 𝑃 ref =𝑃 end , where 𝑃 end is the token price at the end of a control In words, for any outcome 𝑋∈[𝑃 0 ,𝑆], the value deposit forfeit func- period that is not immed{iately fo{llowed by a subsequent auctio}n}. tion must distribute more than (1−𝑡 𝑑)(𝑆−𝑋)𝑞of the value deposit, 𝐷 𝑣, 3. 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 end )=max 0,min 𝐷 𝑣 ,(1−𝑡 𝑑)(𝑆−𝑃 end )𝑞(1+𝜖) . to the 𝑇 1 token holders rather than refunding it to the control party.33 Defining the added amount as 𝛿(𝑆,𝑋), note that all Lemma 1requires In this standard case, a winning bidder who falls short of attaining is that this amount be positive for any 𝑋∈[𝑃 ,𝑆]. Although Lemma 1 a token price equal to the value claim will forfeit to the other token restricts the value deposit forfeit function, the 0 restriction leaves consid- holders an amount just a tiny bit more than the additional gain that the erable latitude. For instance, the mechanism designer can set 𝐷 𝑣 at a o 𝑆 th in er s t t e o a k d e n of h 𝑃 o e l n d d e < rs 𝑆 w . o 31 uld have realized if the token price had reached m im u p c o h s e la h r i g g e h r a v d a d lu it e i o t n h a a l n f o ( r 1 fe − it 𝑡 u 𝑑 r ) e ( s 𝑆 v − er 𝑃 su 0 s ) 𝑞 ( , 1 s − a 𝑡 y 𝑑 ) tw (𝑆 ic − e 𝑋 as ) 𝑞 la o r n g l e y , i a n n c d e r t t h a e in n Some aspects of the standard case can be generalized. Under the ranges within [𝑃 ,𝑆].34 mechanism, the value deposit forfeit function is always set in such a Setting 𝑋=𝑃 0 , a corollary follows immediately from the fact that m th a e n f n u e ll r t g h a a in t t ( h 𝑆 e t − ok 𝑃 e 0 n ) h p o e l r d t e o r k s e o n th o e n r t t h h a e n ir t h (1 e − bid 𝑡 𝑑 d ) er s h w a i r l e l r o e f c e th iv e e t a o t k l e e n a s s t , 𝐷 𝑣 ≥𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆, 0 𝑃 0 ): whether or not the business plan is successfully implemented. If the busi- ness plan succeeds, the other token holders realize the full gain because Corollary 1. If the restriction on the value deposit refund stated in Lemma 1 the market price increases to at least 𝑆, fulfilling the value claim. If is met, 𝐷 𝑣 >(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞. not, the operation of the value deposit forfeit function ensures that any deficit is more than made up from the value deposit.32 Thus, the value This Corollary is the source of the inequality we have used to define deposit combined with the operation of the value deposit forfeit func- the value deposit above. tion transforms the bidder’s value claim into a commitment to deliver We now state the value deposit forfeit function formally and identify the promised increase in token value to the other token holders. The an important special case that is useful as a baseline in what follows: fact that this deposit is held by the applicable smart contract makes this commitment credible and immediately enforceable in a code feasible ⎧ 0 if𝑋>𝑆 ⎪ manner. 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑋)=⎨(1−𝑡 𝑑)(𝑆−𝑋)𝑞+𝛿(𝑆,𝑋) if𝑋∈[𝑃 0 ,𝑆] ⎪ ⎩𝐷 𝑣 if𝑋<𝑃 0 31 An additional property of the standard case is that the value deposit com- bined with the value deposit forfeit function can be conceptualized as requiring the bidder to write an in-the-money bear put spread in favor of the other to- 33 Note that 𝑉 ∈[𝑃 ,𝑆]is private information known only to the bidder. The 0 ken holders consisting of being long a put with strike price 𝑆and short a put at mechanism designer must specify a value deposit forfeit function that achieves strike price 𝑃 <𝑆. the desired result for the case 𝑆>𝑉 regardless of where 𝑉 falls within [𝑃 ,𝑆]. 0 0 32 In cases in which the bidder’s control ends in a subsequent auction, imple- 34 Because the value deposit plays multiple roles, the freedom to set 𝛿(𝑆,𝑋)>0 mentation of any refund may be delayed until after subsequent control periods at will must be applied carefully. For example, if the values of 𝛿(𝑆,𝑋)are set in and may become moot in whole or in part due to the performance of the token such a way that the quantity (1−𝑡 𝑑)(𝑆−𝑋)𝑞+𝛿(𝑆,𝑋)does not monotonically price under the guidance of the subsequent control parties. To the extent the decline over the entire range [𝑃 ,𝑆], then there will be at least subranges in 0 refund is not paid out as part of the transition to the next control period, the which the control party has no incentive to make efforts to increase the value mechanism preserves it as an obligation. See Sections 4.2and 4.3infra. of the DAO. See Section 5.4infra (discussing post-auction incentives). 8 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 where 𝛿(𝑆,𝑋)>0. Define a standard value deposit forfeit function as one 2) If 𝑡 𝑓 ≥0, the DAO Code transfers a total of 𝑡 𝑓 𝑞 tokens from the 𝑇 1 for which 𝛿(𝑆,𝑋) is infinitesimal for all values of 𝑆 and 𝑋. Then for token holdings on a pro rata basis to escrow in the appropriate smart 𝑋∈[𝑃 0 ,𝑆], we have 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑋)≊(1−𝑡 𝑑)(𝑆−𝑋)𝑞.35 contract as part of the bidder’s token deposit, using the purchase Note that if 𝐷 𝑣 >(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞 by more than an infinitesimal deposit to pay each 𝑇 1 token holder 𝑃 0 per token transferred. amount, then there is a discontinuity in the standard value deposit forfeit 3) If 𝑡 𝑓 <0, the bidder has chosen to reduce its holdings from the base- function at 𝑃 0 . Define 𝜙 0 =𝐷 𝑣−(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞to be the baseline loss line token deposit, 𝑡 𝑏 𝑞, by selling |𝑡 𝑓 |𝑞 tokens at price 𝑃 0 , where penalty. As the name suggests, the value deposit forfeit amount jumps by |𝑡 𝑓 |≤𝑡 𝑏. The DAO Code initiates a sales process at 𝑇 1 when the 𝜙 0 when the token value falls below 𝑃 0 and there is a loss relative to the auction ends, making the offering at price 𝑃 0 first to the 𝑇 1 token token price when the auction was initiated. Any outcome less than 𝑃 holders and then to market maker external agents (human or auto- 0 will be penalized by at least this amount. As discussed in Section 5.2, this mated smart contracts), if any, operating under the DAO protocol. baseline loss penalty can be very useful in deterring value destruction. Any proceeds are remitted to the bidder. If tokens remain unsold, Now we discuss the other deposits and the operation of the auction. they remain under the bidder’s ownership as part of the token de- The purchase deposit ensures performance when a bid with 𝑅>0 posit. At the end of this process, the total token deposit is 𝑡 𝑑 𝑞, where commits the bidder to buy 𝑡 𝑓 𝑞tokens at price 𝑃 0 . 𝑡 𝑑=𝑡 𝑏+𝑡 𝑓 ≥0, assuming that all the tokens are sold. The surety deposit addresses the danger that the bidder will engage 4) The DAO Code creates a dynamic vote poo lconsisting of 𝑣 𝑇(𝑞 𝑇 ,𝑡 𝑑 𝑞) in value destruction after gaining control of the DAO. Note that the additional voting rights assigned to the bidder, an amount that surety deposit is reduced to the extent of the value deposit. As will is adjusted continuously based on 𝑞 𝑇, the number of tokens out- become apparent, these two deposits working in conjunction perform standing and eligible to vote at each future time 𝑇, to ensure that three functions: creating optimal bidding incentives, incentivizing per- the bidder retains majority control of the DAO. The required con- formance of the business plan by the winning bidder after the auction dition is 𝑣 𝑇 +𝑡 𝑑 𝑞 >0.5(𝑞 𝑇 +𝑣 𝑇), which can be met by setting ends, and deterring value destruction. The choice of the levels of the 𝑣 𝑇 =max{𝑞 𝑇 −2𝑡 𝑑 𝑞+1,0}, where 𝑞 is the number of tokens out- deposits and the applicable forfeit conditions for each deposit reflect standing and eligible to vote as of time 𝑇 1 when the auction ends. the confluence of these three goals. We discuss the overall role of the The votes in the pool are empty votes because they are not matched surety deposit including the choice and significance of the parameter 𝛾 with the corresponding economic interest inherent in the tokens.38 in Section 5.2after describing the auction mechanism further. Choos- ing optimal levels for the two deposits also depends on the stochastic 4.1.2. The optimal business plan and bidding strategy elements discussed in Appendix A.2. Suppose that a potential bidder can implement a business plan (𝑉,𝐶) Consistent with the lack of centralized management in a DAO, the that involves expending effort, consisting of labor and resources equiv- auction is designed to be self-executing through the Auction Contracts. alent to 𝐶 monetary units, that will result in a token value 𝑉 >𝑃 0 . To reach that goal, the auction mechanism must be code feasible. All This business plan creates social surplus 𝜓(𝑉,𝐶)=(𝑉 −𝑃 0 )𝑞−𝐶. Sup- four deposits are useful in that respect. Because of the purchase deposit pose that among all of the potential bidders’ possible business plans, requirement, nonpayment cannot derail the auction. There is no need the business plan (𝑉∗,𝐶∗)creates the largest amount of social surplus, to have recourse outside of the Code to legal process for purposes of 𝜓∗=(𝑉∗−𝑃 0 )𝑞−𝐶∗.39 collection. As noted in the margin,36 the value deposit, combined with The potential bidder must choose both a business plan (𝑉,𝐶)and a the value deposit forfeit function, plays a role that also could be accom- bid 𝛽(𝑆,𝑅,𝑡 𝑏). It will turn out that the parameter 𝑡 𝑏 is redundant with plished through derivatives. The use of a deposit strategy eliminates respect to winning the auction. Only 𝑆 and 𝑅 matter. The following the need for counterparties and the possible need to enforce counter- Proposition characterizes the optimal business plan and bidding strat- party compliance with the option contracts, which are elements that egy: may not be code feasible without a great deal of added complexity or at all. Similarly, the token and surety deposits substitute for mecha- Proposition 1. Suppose that the condition in Lemma 1that precludes value nisms that would rely on conventional derivative contracts and escrow claims with 𝑆>𝑉 applies. Then the following is the optimal project choice arrangements enforced through the legal system. and bidding strategy for a potential bidder: All four deposits, as well as a valid bid, are required for the bidder (i) Regardless of the bidding strategy chosen, the potential bidder chooses to participate. If the bidder wins the auction, then the DAO Code uses the business plan (𝑉∗,𝐶∗)that results in 𝜓=𝜓∗, the largest possible social the purchase deposit to acquire the freeze-out proportion of tokens for surplus that the potential bidder can generate subject to the market liquidity transfer to the winning bidder and retains the other three deposits, re- constraint, 𝑡 𝑑=𝑡 𝑓 +𝑡 𝑏 ≤𝑡 𝑚. If 𝜓∗≤0, the potential bidder does not make turning them if and only if certain conditions are met. If the bidder loses a bid. the auction, all four deposits are returned. The auction is closed at time 𝑇 , a date which is analogous to a record 1 date in corporate stock transactions, and the following Auction Closing 38 The choice of giving the winning bidder majority control (>50% of the Steps are implemented instantaneously:37 votes) implicit in this arrangement leaves open the possibility that the winning bidder will not be able to prevail on DAO issues that require a threshold greater 1) T ot h h e e r D t A h O an C t o h d e e b i i d d e d n e t r i ’ fi s e t s o k to e k n e d n e h p o o l s d it e r a s s o o f f t t h im e e ( 1 𝑇 − 1 , 𝑡 c 𝑏 o )𝑞 lle t c o t t i a v l e t l o y k , e th n e s t t in h h g e a n D t h 5 A r 0 e O % s h C o t o o l d d p e s a a f s o n s r d t h th t e h e a e v p a o p s t l s e i o c a c p b i o a l o t e e l d p n r e o is e p s d u o s s e a t s o l . s e b T t e h f e s o e e r n x s t a h it c e i t v D p e e A t r o O c e t n h m t e a o g r h e e i e g e r s a e t n r a c e b h r l y a is l l h o y e f . d v I f o b t y a - 𝑇 1 token holders who hold the 𝑇 1 token holdings. less conventional choice method, such as quadratic voting, is employed by the DAO, the dynamic voting pool must grant whatever number of additional voting rights is required to establish control. 35 The standard value deposit forfeit function is equivalent to the value deposit 39 We assume that the auction takes place in a “private values” setting with forfeit function used to define the standard case above. asymmetric information. Each bidder’s potential set of business plans and their 36 See Footnote 31supra, which states the equivalent derivatives position for value-enhancing potential are known only to the bidder. All bidders agree on the a case in which that position is a simple options spread. In general, there will value of the current operation. If there is a common values element in which bid- be an equivalent derivatives position, but it may not be simple. ders have different signals concerning the value of the current operation and bid 37 Blockchain technology allows for continuous identification of token hold- based on perceived undervaluation at price 𝑃 , then the efficiency and surplus- 0 ings, and the steps outlined below can be implemented through smart contracts distribution characteristics of the auction mechanism may be affected. However, instantly with respect to the token holdings as of time 𝑇 when the auction choosing the English auction as a mechanism tends to make any such impacts 1 closes. benign or even beneficial. See Footnote 63infra. 9 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 (ii) The bid parameters that result in the strongest possible bid are: be large enough to cover the cost 𝐶 minus the gains on the toehold 𝑆=𝑉∗; and (𝑉 −𝑃 0 )𝑡 𝑏 𝑞, i.e., 𝑅=𝐶−(𝑉 −𝑃 0 )𝑡 𝑏 𝑞. Then, 𝐴=(𝑉 −𝑃 0 )𝑞−𝐶, which 𝑅=𝐶∗−(𝑉∗−𝑃 0 )𝑡 𝑏 𝑞 is equal to the total social surplus. Clearly, the best possible bid will re- which result in an auction parameter equal to 𝐴∗, the largest possible social quire choosing (𝑉∗,𝐶∗), the business plan that maximizes total social surplus that the potential bidder can generate subject to the market liquidity surplus subject to being feasible in the face of the market liquidity con- constraint: straint. That constraint allocates at least the proportion 1−𝑡 𝑚 of the 𝐴∗=(𝑉∗−𝑃 )𝑞−𝐶∗=𝜓∗. total added token value to the 𝑇 token holders, who are free riders be- 0 1 This bid results in zero profit for the potential bidder, with all of the social cause they bear none of the cost of adding value. The constraint may surplus being shifted to the other token holders. bind in the optimization that determines (𝑉∗,𝐶∗). The choice of 𝑡 𝑚 <1, therefore, may preclude execution of the optimal business plan from a (iii) If a profit level Π𝑏is feasible given the market liquidity constraint, then social perspective. the strongest possible bid parameters are: 𝑆=𝑉∗; and whic 𝑅 h = re Π su 𝑏 lt + in 𝐶 t ∗ he − f ( o 𝑉 llo ∗ w − in 𝑃 g 0 a )𝑡 u 𝑏 c 𝑞 tion parameter: C 𝑡 𝑚 o < ro 1 ll , a t r h y e n 2 t . h I e f b th id e d m er a w rk i e ll t c li h q o u o i s d e i t a y b c u on si s n t e ra ss i n p t l , a 𝑡 n 𝑓 t + ha 𝑡 t 𝑏 f ≤ all 𝑡 s 𝑚 s , h i o s r b t i o n f d i c n r g e a w ti i n th g 𝐴(Π𝑏)=(𝑉∗−𝑃 0 )𝑞−𝐶∗−Π𝑏=𝜓∗−Π𝑏. the greatest possible social surplus. T m h a i i s n i b n id g s r o e c s i u a l l t s s u in rp p lu r s o , fi 𝜓 t ∗ eq − ua Π l 𝑏 t , o s h Π if 𝑏 te f d o r t o t h th e e p o o t t h e e n r t i t a o l k b e i n d d h e o r l , d e w r i s t . h the re- 𝐴∗ 𝑖. S I u n p p a o n s e E n t g h l a is t h t h a e u r c e t io a n re , t 𝑛 he b i h d i d g e h r e s s t a b n i d d d th er a t w b il i l d d p e re r v 𝑖 a ’s il b a e t s t t h b e id se c is - (iv) The largest obtainable profit level is Π𝑏=𝑡 𝑚(𝑉∗−𝑃 0 )𝑞−𝐶∗≤𝜓∗given ond highest bidder’s submitted auction parameter. The highest bidder t 0 o < ke 𝑡 n 𝑚 h < ol 1 d . e r T s h i e s m 𝐹 in = im (1 um − 𝑡 s 𝑚 oc )( ia 𝑉 l ∗ su − rp 𝑃 lu 0 ) s 𝑞 t . hat must be transferred to the other c th a e n h p i r g e h v e a s il t w bi i d th d e a r ’s b i b d e s o t f p a o t s m sib o l s e t b 𝐴 i 1 d. = T 𝐴 h ∗ 2 e , n , a n s d u b t j y e p ct i ca to ll y t , h e 𝐴 1 m < ar 𝐴 ke ∗ 1 t , liquidity constraint, the highest bidder can increase 𝑅 from its level Leaving a formal proof to Appendix A.1, we outline the proof here 𝑅∗=𝐶∗−Π𝑡𝑏 , where Π𝑡𝑏 =(𝑉∗−𝑃 0 )𝑡 𝑏 𝑞is the bidder’s toehold profit, to with an emphasis on intuition and then discuss the significance of the 𝑅∗+min{𝐴∗ 1 −𝐴∗ 2 ,𝑁∗−Π𝑡𝑏 −𝐶∗−𝐹}. The term 𝑁∗−Π𝑡𝑏 −𝐶∗−𝐹 is results. the maximum possible value of 𝑅that is feasible under the market con- The potential bidder’s highest surplus business plan produces total straint given 𝐹, the minimum surplus that must be delivered to the free added token value of 𝑁∗=(𝑉∗−𝑃 )𝑞at cost 𝐶∗. The potential bidder riders. 0 will realize the proportion 𝑡 𝑑=𝑡 𝑓+𝑡 𝑏 ≤𝑡 𝑚of this added value through This algebraic exposition can be visualized through a series of fig- a toehold of 𝑡 𝑏 𝑞tokens acquired before the auction plus 𝑡 𝑓 𝑞tokens ac- ures. quired at 𝑃 from the 𝑇 token holders using the freeze-out feature of the In Fig. 1, the business plan (𝑉,𝐶)induces a value claim 𝑆=𝑉 and 0 1 auction mechanism. The parameter 0<𝑡 𝑚 <1guarantees that the 𝑇 1 to- a surplus claim value of 𝑅just big enough to cover the cost 𝐶, which k t F o e o k n r e h a n n o v l y d a e l fi u r x s e e w d as il l l f e r r v e e e e c l e r o i i v d f e e 𝑆 r a s , t u l c e h n a o d s o e t r s t i h n t e h g e p 𝑅 r a o u p i c s o t i r e o t q i n o u n m iv 1 e a c l − e h n 𝑡 a 𝑚 t n i t o s o f m t c , h h e 𝑡 o 𝑓 t o o = s t i a n ( l g 𝑆 a − 𝑅 d 𝑡 𝑃 𝑓 d 0 , ) e 𝑞 d a . r t in o e s k t u e h l n e t s h b i o i n d l d d t e h e r r e s r w t e h a i r n l o i n z u i i n g n g h g b a th d id e d d e f e r d e r e t p o z u k e r - e o c n h u v a t a s m i l n u e g e c h 𝑡 e 𝑓 a q n 𝑞 u i a s t l o m k t . o e T n t h h s i e a s t b p l 𝑃 u u 0 r e c f h r r e a o c s m t e a n r t e h g s e l u e l 𝑇 𝑅 t 1 s residual that completely determines the division of the total added to- in the figure. The green rectangle Π𝑡𝑏 is the added token value that the ken value between the control party and the free riders. For this reason, bidder realizes from the toehold position 𝑡 𝑏 𝑞. The bidder’s total added the fixed toehold proportion 𝑡 𝑏is irrelevant to division of the total added token value is the sum of the green and blue rectangles, which is equal token value, which depends on 𝑡 𝑑=𝑡 𝑏+𝑡 𝑓, where 𝑡 𝑓 is freely chosen in this instance to the red rectangle representing the cost 𝐶. The area 𝐹 subject only to −𝑡 𝑏 ≤𝑡 𝑓 ≤𝑡 𝑚−𝑡 𝑏. in the figure represents the minimum added token value that must be Consider the auction parameter: granted to the other post-𝑇 1 token holders, the proportion 1−𝑡 𝑚of the total, and these free-riding token holders also realize that added token 𝐴=(1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞−𝑅=(1−𝑡 𝑓−𝑡 𝑏)(𝑆−𝑃 0 )𝑞. value is equal to the unlabeled white rectangle between the 𝑅rectangle and the 𝐹 rectangle. It is clear that 𝐴is increasing in 𝑆 holding 𝑡 𝑓, and thus, the potential If 𝐴∗>𝐴∗, the winning bidder will be able to appropriate part or bidder’s share of the total added token value is fixed. This fact tells us all of th 1 e add 2 ed token value represented by the white rectangle. Fig. 2 that the bidder will choose 𝑆≥𝑉. The remaining question is whether illustrates the case where the winning bidder is able to appropriate part the bidder would ever opt for a value claim greater than 𝑉. but not all of it. To examine that question, consider the potential bidder’s profit func- These figures illustrate a key feature that enables the mechanism to tion expressed in terms of 𝑡 𝑓 when the potential bidder implements a work. Burkart and Lee [33] showed that in deterministic tender offer business plan (𝑉,𝐶): games, the ability to relinquish private benefits might be necessary for Π𝑏=(𝑉 −𝑃 0 )(𝑡 𝑓+𝑡 𝑏)𝑞−𝐶−𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑉). t a h ll e o w ex s i s b t i e d n d c e e r s o f t o a r s e e l p in ar q a u t i i s n h g b e e q n u e i fi lib ts r i b u y m c . h T o h o e s i a n u g c 𝑅 tio , n th m e e s c u h r a p n lu is s m c l h ai e m re . The first term is the added token value realized by the potential bid- A lower value of 𝑅 results in a stronger bid but a smaller amount of der, the second term is the potential bidder’s project cost, and the third added token value accruing to the bidder. Because of the freeze-out fea- term is the expected value deposit forfeit that will result from choosing ture of the mechanism, the possibility that free-riding will undermine 𝑆>𝑉 when the highest token value the bidder can achieve by execut- signaling is eliminated. The bidder can specify an exact claim, 𝑅, to ing the business plan is 𝑉. This expected value deposit forfeit requires added token value that otherwise might be inaccessible due to free rid- a larger surplus claim, potentially weakening the bid. However, over- ing. Combined with the basic auction features that make revealing 𝑉∗ bidding by choosing 𝑆>𝑉 also increases the first term in the auction truthfully a dominant strategy, the flexibility with respect to 𝑅sets up parameter, which admits a larger surplus claim. Resolving the impact of an effective signaling environment that leads to a separating equilib- this tradeoff requires mathematical analysis. Lemma 1, set forth in the rium. previous subsection, states restrictions on the value deposit forfeit func- 𝐴∗ proxies for bidder types, and a bidder with a lower 𝐴∗ cannot tion, under which choosing 𝑆>𝑉 means that earning the same amount profitably mimic one with a higher 𝐴∗. For bidder 𝑖, the strongest pos- of surplus requires a weaker overall bid compared with choosing 𝑆=𝑉. sible bid, 𝐴∗ 𝑖, is associated with zero profits. A higher bid results in net The strongest possible bid subject to the value deposit forfeit func- losses. As the English auction unfolds, if each bidder 𝑖 moves up until tion restrictions will minimize 𝑅in addition to setting 𝑆=𝑉. 𝑅must the level 𝐴∗ 𝑖 and then drops out, 𝑉 𝑖 ∗ and 𝐶 𝑖 ∗ will be evident because 10 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 Fig. 1 .Structure when the winning bidder only covers cost. Fig. 2 .Structure when the winning bidder appropriates some of the social surplus. the bid also reveals 𝑡 𝑏.40For the winning bidder, only 𝑉 1 ∗and an upper sion in second-price auctions. If there are 𝑛 bidders, then conditional bound on 𝐶∗will be evident because it is possible that the winning bid on winning the auction, bidder 1 expects to capture added value equal 1 c 𝐴 e 1 iv < in 𝐴 g ∗ 1 m s o o r e th a a d t d Π ed 𝑡𝑏 t + ok 𝑅 en 1 > va 𝐶 lu 1 ∗ e . t I h n a t n h a is t n c e a c s e e s , s t a h r e y w to i n in n d in u g c e b t id h d at e r b i i d s d r e e r - t is o t 𝐴 h ∗ 1 e − ex 𝐸 p ( e 𝐴 ct ∗ 2 ed | 𝑛 va − lu 1 e a o n f d t 𝐴 he ∗ 2 ≤ hig 𝐴 h ∗ 1 e ) s . t T o h r e d e e r x p s e ta c t t i a s t t i i o c n o i f n t t h h e i s o e th xp er r e 𝑛 ss − ion 1 to implement the best possible business plan. This situation appears to values of 𝐴∗ 𝑖 ≤𝐴∗ 1 . If a group of bidders collude, only the bidder with fall short of the first best, which requires that all of the social surplus the highest value among them will bid. That strategy eliminates all the remains with the free-riding token holders in order to optimize initial other bidders in the group from potentially lowering the highest bidder’s and on-going investment in the DAO. But, as discussed in Section 5.1, added value from winning by submitting the second highest bid. If the the full picture is more complex. collusion group is a subset of size 𝑛 𝑐 ≤𝑛−1, then the expected added value capture is with respect to a highest order statistic of a smaller 4.1.3. Bidding intensity, group bidding, and collusion number of other bidders, 𝑛−𝑛 𝑐−1 instead of 𝑛−1, and therefore is Two elements that are relevant to the investment impact of the higher. In the extreme situation in which all bidders collude effectively, mechanism are bidding intensity and the possibility of collusion among the highest bidder can prevail with a bid just above 𝑃 0 , thereby extract- bidders. Krishna [34, Chapter 11] lays out basic points about collu- ing the proportion 𝑡 𝑚 of the total gain, the maximum possible subject to the market liquidity constraint. The winning bidder then splits the added value from collusion with the other colluding bidders, a division that motivates them to be part of the collusion group. s 4 u 0 bm As it t d in is g c u a s s b e i d d i w n i S th e c 𝐴 tion > 4 𝐴 .1 ∗ .6 b , y i t u i n s d p e o rs s t s a ib ti l n e g t h th a e t t s h u e r p s l e u c s o n cl d a i h m ig r h e e q s u t i b re id d d t e o r Collusion, especially involving more than a few potential bidders, break even is a profitable 2 strate 2 gy. Although the bidder risks an operational loss requires costly coordination, but if it occurs, it will impact investment if the bidder wins the auction, the bidder will retain a larger proportion of its negatively. Collusion results in winning bidders extracting more added toehold and earn the ensuing profit per token, 𝑉 −𝑃 , on that larger position value, reducing the attractiveness ex ante for initial and on-going invest- 0 if it loses. The winning bidder faces a higher floor, 𝐴 >𝐴∗, instead of 𝐴∗, and ment. There are some situations in which collusion is a very plausible cannot claim as much of the available social surplus i 2 n tha 2 t instance. 2 threat. For example, if there is a strong outside candidate to add value 11

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 through an innovative business plan, the most likely competing bidders 4.1.4. Toehold reporting and post-auction market dangers may be a handful of identifiable “insiders” who previously had been The basic auction mechanism requires that the bidder report any the most active in directing the DAO. Small numbers make collusion toehold position as part of the bid for two reasons. First, an accurate re- easier to coordinate, and if the small group includes the likely highest port of the toehold is necessary for the mechanism to work as intended. set of bidders, collusion is likely to be very effective. The fact that DAOs The mechanism is designed to rank bidders based on how much social have been characterized by low participation rates and a few key players surplus they can offer the other token holders. To calculate the social running the show suggests that this situation may be common. Outside surplus offered by a particular bid, it is necessary to subtract two quan- candidate collusion with the insiders creates a substantial opportunity tities from the total added token value, (𝑆−𝑃 )𝑞, that the bidder asserts 0 for reducing the social surplus that otherwise would accrue to the other will be created. One is (1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞, the portion of the added token token holders. value that the bidder will capture through the bidder’s toehold position. A key parameter is the expected bidding intensity. If there is a con- The second is the bidder’s surplus claim. These two quantities flow to tinuum of potential bidders who have values of 𝐴∗that are dense in the the bidder and not to the other token holders. For a rational bidder, the interval [0,𝐴∗], then it will be impossible to collude, and winning bid- sum of the two quantities will at least cover the bidder’s costs, and to 1 ders will only be able to cover their cost. Investment incentives will be the extent the sum exceeds the two quantities, the bidder will appropri- maximized. If there are only a handful of potential bidders, then col- ate some of the social surplus. If the bidder hides the toehold position lusion will be a bigger danger, and, even in the absence of collusion, by not reporting it, the bidder will be claiming to transfer more social the winning bidder will be likely to walk away with considerable extra surplus to the other token holders than is actually the case. Part of the social surplus to the detriment of investment. claimed transfer of social surplus to the other token holders will actu- Bidding intensity and the viability of the mechanism itself depend on ally be retained by the bidder. The bid will have an artificial advantage. capital market adequacy, the depth and development of capital markets. If this bidder wins, it may be the case that some other bid promised to Making a bid through the mechanism requires deposits of the same order deliver more actual social surplus to the other token holders, subverting of magnitude as the total pre-bid value of the DAO. For established DAOs the operation of the auction mechanism.44 such as Uniswap, Maker, or Compound, deposit amounts of a billion dol- Second, the true value of the toehold proportion, 𝑡 𝑏, is necessary lars or more may be required.41 A deep bench of institutional, such as to enforce the market liquidity condition 𝑡 𝑏+𝑡 𝑓 ≤𝑡 𝑚, which guarantees venture capital firms, private equity firms, and hedge funds, is required that at least (1−𝑡 𝑚)𝑞tokens are held by others, creating a pool of market to make the auction mechanism robust and create bidding intensity. At liquidity. Relevant to both purposes, nothing in the bidding mechanism least on the venture capital front, a large number of such firms already itself creates an incentive for a true report, and, in fact, the incentive is exist and are very active with respect to cryptocurrency projects includ- to cheat by hiding some of the toehold to artificially inflate the bid, 𝐴. ing many DAOs [36]. These firms would be a ready source of funding Effectively addressing potential toehold concealment depends both for auction bidders. The temporary contestable control created by the on the identifiability of the control party’s token holdings, defined as the auction mechanism, if implemented, might itself spawn specialist insti- ability to associate positions with the control party, and on the costs tutions similar to hedge funds in the current corporate landscape that of doing so. Complicating matters, any identification method must be combine portfolio investment with selective activism in governance.42 EV-robust. The potential threat is from hidden ownership, which is, as One aspect of the auction mechanism is highly relevant to the possi- discussed in the introduction, the obverse of empty voting. Instead of bility of collusion. There is nothing that prevents group bidding. A pool voting with no economic ownership, hidden ownership involves eco- of outsiders, of insiders, or a mixture of both might combine into a bid- nomic ownership without voting. It can easily be implemented via an ding entity. It is possible to implement this combination via a smart equity swap between the control party and a token holder. In exchange contract, with the parties contributing the required stablecoins to fund for the economic interest in the DAO, including token appreciation, the bidding and then jointly holding the control position if their bid prevails. control party offers another economic position, such as treasury bond re- Group bidding may facilitate collusion, but it also may add valuable bid- turns, to the token holder. The token holder continues to own the token ders who otherwise would not participate. For example, an entrepreneur and will be identified as the owner on chain, but, secretly, the control with promising innovative ideas for running the DAO but with limited party is able to overstate the social surplus being offered to the other resources could form a bidding entity with private equity or venture token holders by not reporting the associated economic position as part investors who could fund the project. As described by Krishna [34], collusion in English auctions typically of the control party’s toehold. This maneuver may be very hard to de- is illegal or subject to civil penalties in the non-digital world, but it tect. In effect, a much deeper level of identification is required, one that is hard to see how collusion might be detected and policed in a code reaches beneath formal ownership. feasible manner. Group bidding via smart contracts may be detectible, Potential concealment of part or all of a toehold position is not the but whether it is merely collusive, has bid-formation advantages, or is only threat that creates a need for identification. There are possible dan- a mixture of the two would be a complex inquiry, requiring something gers arising from post-auction market manipulation by control parties. If akin to legal processes. Although there are mediation and adjudication the market is thin enough, the control party can engage in focused buy- tools available apart from the legal system, using these tools adds an ing to drive the market up to levels that substantially reduce the value or additional element of complexity and requires trust in the tools.43 surety deposit obligations at the time when those obligations are mea- sured and enforced, and then engage in selling to reverse the temporary 41 As of November 24, 2024, these three DAO governance tokens had market capitalizations of approximately $6.4 billion, $1.5 billion, and $580 million, hicles, including Kleros, for DAOs generally, noting that they are most effective respectively, according to CoinMarketCap [35]. when remedies can be executed on-chain because the parties have assets at risk 42 Yin and Zhu [37]provided an empirical analysis. Such hedge funds typi- there. In the case of collusion, some relevant parties may not. cally engage in activism with respect to only a small portion of their portfolios. 44 All this is evident from Figs. 1and 2in Section 4.1.2supra. In the figures, the Burkart and Lee [29]summarized the evidence that takeover activism aimed at white portion plus the gray portion of the top rectangle is the amount of social or resulting in changes in corporate control generate higher target and activist surplus the bidder is claiming to transfer to the other token holders. The green returns. portion of the top rectangle is the portion of the total added token value that the 43 A prominent example of a mediation and adjudication tool is Kleros [38]. bidder will realize on the bidder’s toehold position. Hiding this green portion Greig [39]described how Kleros operates by rewarding jurors for their perfor- by not reporting it falsely represents that it is social surplus being transferred to mance based on a Schelling point criterion. Kleros is active, with multiple open the other token holders, making it appear to be part of the white portion of the cases [40]. Guillaume and Riva [41]discussed the use of dispute resolution ve- upper rectangle. The bid appears to be better than it really is. 12 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 position, similar to a pump and dump.45 Whether the market is robust tially a very powerful deterrent. Successful bounty recovery is a disaster or not depends both on the market capitalization of the DAO token and for the winning bidder, involving loss not only of potential added token on the proportion of tokens not held by the control party.46If the mar- value, the motivation for concealment, but also of the base value, 𝑃 . 0 ket liquidity constraint is binding, the control party will exit the auction One set of approaches to address control party position reporting is- with the maximum proportion of 1−𝑡 𝑚of the total tokens outstanding, sues centers around using know-your-customer registration systems that a situation that increases the danger of manipulation because of reduced make token holders identifiable. Requiring registration of all token po- market liquidity stemming from a lower traded-token supply. If the ma- sitions at all times would be very costly both initially and in the face of nipulation danger is salient enough, then for the auction mechanism to continual revisions as tokens are traded between parties. Registration work, it may be necessary to bar the control party from the post-auction might also raise privacy considerations requiring costly zero-knowledge market. Enforcing this bar would rely on an identification procedure proof or other technologies to make identities private yet verifiable. that could operate effectively during the control period in the face of Nonetheless, use of registration limited to subsets of token holders and control by the control party.47 to particular points in time might be useful and cost-effective, as we For an identification method to work in a decentralized framework, describe in what follows. it must be code feasible as well as effective. We consider some possi- One particularly promising way to address the toehold reporting ble methods in what follows, concluding with what appears to be the problem is to use a flush sale variant of the mechanism. This variant most promising one. We focus on the problem of concealment of a toe- is characterized by the following differences from the mechanism de- hold position. The discussion applies in an obvious way to attempting scribed so far: to enforce a bar on market participation. One method of identification is a bounty system. Any party that dis- 1) Revised purchase deposit. The purchase deposit is 𝐷 𝑝 𝑓 =(1−𝑡 𝑏)𝑃 0 , covers and proves that the winning bidder concealed part of the toehold covering all the tokens other than the reported toehold position con- rather than reporting it would be awarded a number of tokens with cur- sisting of 𝑡 𝑏 𝑞tokens. rent value equal to the value of the concealed part of the toehold at 𝑇 0 , 2) Flush sale. The DAO Code uses this deposit to purchase all of the the time of concealment, while simultaneously burning the correspond- tokens other than the reported toehold at price 𝑃 . This purchase 0 ing quantity of concealed tokens held by the control party. If the value implements the flush sale. of the concealed tokens at the time the bounty is granted is less than 3) Adjusted token deposit. The DAO Code adds or subtracts tokens from their 𝑇 0 value, the shortfall can be made up by burning part of the con- the token deposit to adjust that deposit by the quantity 𝑡 𝑓 𝑞. trol party’s token deposit or by creating debits against the control party’s 4) Token auction. At the end of the basic auction, the DAO Code ini- stablecoin deposits. tiates a token auction, selling (1−𝑡 𝑑)𝑞 tokens using a hard-coded Could a bounty system be effective and code feasible? DAO positions auction technology that aims at revenue maximization. Purchases appear as a set of public addresses and token quantities. Commercially by the control party are barred, enforced to the extent feasible by a available technologies to trace and attribute token ownership exist and registration system. have a significant degree of effectiveness at what may be feasible cost 5) Registration. Parties can register through a know-your-customer pro- [43]. But reliance on outside commercial parties inhibits code feasibil- cess to demonstrate that they are not the control party or related to ity. The DAO may have to implement the bounty system via contracts the control party.50 All registered parties are eligible to participate with outside teams. Doing so effectively while the control party has in the token auction. The set of 𝑇 token holders who register will 1 control of the DAO may not be possible. The task is complicated by be eligible to receive surplus from the auction. the possible need to resolve disputes about the veracity of identifica- 6) Treatment of token auction surplus or deficit. A token auction deficit tions claimed by the bounty hunters.48And possible hidden ownership caused by an average token auction price below 𝑃 remains a liabil- 0 presents a major challenge to the effectiveness of bounty systems.49 ity of the DAO. Any token auction surplus is distributed pro rata at Although a bounty system may be too difficult to implement, it is poten- a specified flush sale surplus distribution date to the set of registered 𝑇 token holders based on their relative 𝑇 holdings. This date is set 1 1 by the DAO Code to give sufficient time for 𝑇 token holders to reg- 1 45 The value deposit and surety deposit obligations are measured and forfeiture ister before the flush sale surplus distribution date if they did not do of part or all of the deposits is possible at control transition points. Sections 4.2 so prior to the token auction. and 4.3 describe and discuss the various transition points including the end o b f e f c o o r n e t t r h o e l t p im er e io l d im s i b t y is t r i e m a e c h li e m d, i t a , b s a u n b d s o e n q m ue e n n t t a o u f c c t o io n n tr s o t l h d a u t r i e n n g d a c c o o n n t t r r o o l l p p e e r r i i o o d d s , The flush sale variant attempts to address the problem of non-reporting and the success termination of a control period based on attaining the token of the full extent of the winning bidder’s token position. Some or all of target price established by the value claim for a sustained period of time. it is hidden among the 1−𝑡 𝑏proportion remaining after the proportion 46 Hamrick et al. [42] provided substantial evidence that pump and dump 𝑡 𝑏 is declared and deposited. The flush sale is just that: It flushes out manipulations are much harder, as measured by the induced percentage price any hidden control party positions among that remaining proportion by increase, for heavily traded, high market capitalization cryptocurrencies. forcing sale of the entire remaining proportion at 𝑃 0 . 47 Identification in the face of market manipulation not only would facilitate It is likely that the auction purchases will be at prices significantly countermeasures internal to the DAO but also would empower external actors higher than 𝑃 . For that reason, even without the success of a bounty sys- who have prosecution and enforcement authority. In the United States, for in- tem, registrat 0 ion, or similar measures, the winning bidder is faced with stance, the Commodities Futures Trading Commission has the power to police a potential reduction in added token value on any positions that were m tio a n rk 5 e . t 6 m in a f n ra ip . ulation for almost all publicly traded cryptocurrencies. See Sec- concealed even if accompanied by corresponding repurchases after com- 48 Dispute resolution is more difficult when the parties do not have accessible pletion of the token auction. In contrast, declaring and depositing the on-chain assets at risk. See Footnote 43supra. An approach such as requiring pre-auction positions puts them in a safe harbor that allows the winning good faith deposits from bounty hunters might be required to implement a dis- pute resolution mechanism that is code feasible. 49 Bounty hunters do have some possible strategies in the face of hidden own- 50 Registration can be made consistent with privacy through approaches such ership. Counterparties to the hidden ownership position used for concealment as requiring a zero-knowledge proof confirmation that they are not a restricted have an incentive to collect the bounty by disclosing the failure to report, po- party linked to the winning bidder. For example, Rosenberg et al. [44]described tentially earning additional tokens at the expense of the control party without a zero-knowledge proof credentialing system that they called “zk-creds.” In one violating the underlying contract. Bounty hunters may angle for a cut by adver- instantiation, parties embed their passport in a zero-knowledge privacy layer tising this opportunity broadly and offering assistance. that allows proof of identity. 13 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 bidder to collect 100% of any added token value that arises. The reg- with making a bid, the potential bidder can purchase a suitable quan- istration system is crucial for establishing these incentives because the tity of out-of-the-money call options with a strike price of 𝑉∗. If the 𝑏 system ensures that any added token value from the auction flows to 𝑇 bidder loses and the winning bid includes a value claim 𝑉∗>𝑉∗, then 1 𝑏 token holders other than the control party. Registration for participation the call option will yield what would have been the toehold profit. If in the token auction also plays a role because market trading after the the bidder wins, the bidder can liquidate the call option position, most auction is likely to be accompanied by substantial additional demand likely at a profit because it is plausible that the token price will be for tokens and a corresponding sharp price increase similar to what greater than 𝑃 0 when the auction closes at 𝑇 1 , and possibly substan- happens in a successful initial public offering in equity markets. Reg- tially greater. istration requirements block control parties from enjoying these gains. Use of a registration system aimed at blocking control parties from mak- 4.1.6. Auction efficiency and market liquidity ing auction purchases is likely to be particularly effective compared to Like second-price auction frameworks in other contexts, the English alternatives such as relying on bounty hunters, and because it would be auction that embodies the basic mechanism here has strong efficiency limited in scope, relatively low cost. properties. The bidder who can produce the most social surplus wins, Flush sales implemented using registration can be combined with with appropriation of that surplus by the winning bidder limited by the bounty hunting or other measures aimed both at the pre-sale concealed level of the second highest bid. As discussed, there is another limita- positions and at any purchases during the token auction. More than tion: The mechanism is subject to the market liquidity constraint. This one such measure may be employed simultaneously. For the flush sale constraint limits the added token value available to the winning bidder, variant to be successful, registration and any other accompanying mea- reducing it by 𝐹 =(1−𝑡 𝑚)(𝑉∗−𝑃 0 )𝑞, the minimum amount that must sures combined with the safe harbor aspect of reporting must make accrue to free riders. Consider the project (𝑉∗,𝐶∗)that creates the high- concealment in order to improve the bid, 𝐴, unprofitable, unattractive, est possible social surplus 𝜓∗=𝑁∗−𝐶∗and produces total added token or infeasible. The stakes are significant. To the extent that the winning value 𝑁∗=(𝑉∗−𝑃 0 )𝑞. If 𝜓∗=𝑁∗−𝐶∗>0>𝑁∗−𝐶∗−𝐹, then this bidder can evade reporting the toehold position, it will gain an artificial best possible project will not be implemented because it cannot cover bidding advantage equal to the amount of added token value associated its cost and also distribute 𝐹 to the free riders. with the concealed position. Auction efficiency is imperiled because a The purpose of the constraint is to enable the token market to operate bidder with a larger toehold may prevail over another bidder who has continuously, which is important because the market value of the DAO a superior business plan. tokens is a key input for the auction mechanism. Other approaches are possible, but it is not clear that they would resolve the trade-off between 4.1.5. The role of the toehold and activism strategies having a continuous active market and avoiding the danger that some Toeholds play a crucial role in the current market for corporate socially valuable projects will be precluded by free riding that limits the control. Burkart and Lee [29]showed that under current law, both ac- available added token value. One possibility is a variant of the flush sale tivists and tender offerors profit primarily from toeholds in the face of and subsequent token auction discussed in Section 4.1.4. If the market Jensen-Meckling and Grossman-Hart free riders, respectively. Further- liquidity constraint is binding, then the flush sale at price 𝑃 0 consists more, Burkart and Lee [33]proved that the toehold can play a signaling of the (1−𝑡 𝑚)𝑞 tokens that are not held by the winning bidder at the role because choosing the level of the toehold is a way to claim or re- conclusion of the auction. The variation applied when the constraint is linquish control benefits. binding is that instead of surplus from the token auction being directed Under the basic auction mechanism, there is no reason for a potential to the 𝑇 1 token holders, it would be paid, up to the amount 𝐹, to the bidder to accumulate or add to a toehold if the potential bidder is con- winning bidder, giving that bidder some or all of the added token value fident of winning the auction and toehold reporting is enforceable. The that previously would have flowed to the free-riding 𝑇 1 token holders. At size of the toehold does not affect bidding strength or potential profits. the same time, the token auction would reestablish market liquidity.51 When a potential bidder is contemplating initiating an auction, buying It is unclear what portion of the missing added token value, 𝐹, that the more tokens to accumulate a bigger pre-auction toehold is a dominated winning bidder would in fact realize from this forced sale plus token strategy. Doing so will only drive up the price during accumulation when auction approach. Market participants might be skeptical of the ability the potential bidder can use the freeze-out feature of the basic auction of the winning bidder to fulfill the 𝑉∗value claim by bringing the token to force sale of the tokens at the lower pre-accumulation price. Further- value to that level. Addressing this situation by allowing the winning more, any potential signaling role of the toehold is extraneous because bidder to delay the forced auction to create time to demonstrate the the basic auction allows the bidder to claim or relinquish control bene- value of the business plan would create a period with no market prices. fits directly. There is another possible source of inefficiency, which we will call One remaining question revolves around the role of traditional ac- “toehold overbidding.” Burkart [45]showed that in an English auction, tivism in which the activist buys a toehold and then engages in a costly it may be optimal for participants with toeholds to bid higher than their campaign to influence management. In the case of a DAO, the targets valuations. Overbids create a danger of overpaying if the overbidder of influence would be the control party during a control period and the wins, but they also may push up the winning auction price, benefiting most active governance parties otherwise. If the activist has a concrete the toehold position if the overbidder loses. Burkart [45]proved that, value-increasing plan that the activist could implement alone or after as- in the context of his model, for sufficiently small overbids, the potential sembling a bidding group, the activist is better off initiating an auction toehold benefit outweighs the danger of loss from winning the auction if the activist is confident of winning. The activist could acquire tokens with an overbid.52 more cheaply through the auction freeze-out feature than by buying a The mechanism developed here eliminates the incentive to make toe- toehold and would not have to incur campaign costs to convince the hold overbids. Bidders are competing to offer as much added token value control party or the active governance parties to adopt the activist’s to the other token holders as possible. There are two ways to offer more business plan. Any potential bidder, activist or not, has to consider the possibility of losing the auction that they initiate. Losing the auction means there t 5 o 1 b A lo c b k o u th n e ty w s i y n s n te in m g o b r i d a d lt e e r r f n r a o t m iv e p a e r n t f i o ci r p c a em tin e g n t i n m t e h c e h t a o n k is e m n a w u o c u ti l o d n b d e i r r e e c q t u ly ir . ed was a higher bid, and if the winning bidder’s business plan is credi- 52 The potential gain on the toehold is of the order of magnitude of the over- ble, then a losing bidder can profit from a toehold position. However, bid, while the potential loss from the overbid is of the order of magnitude of there are better ways than a toehold position to insure against losing the overbid squared. Burkart [45]assumed a private values setting in his main the auction. Suppose that the potential bidder contemplates a bid that inquiry. Bulow et al. [46]showed that toehold overbidding tends to be a much includes a value claim 𝑉 𝑏 ∗ when the token price is 𝑃 0 . Simultaneously more serious problem in common values situations. 14

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 added token value: through a higher value claim or a lower surplus 1) The dynamic vote pool is closed, removing all the empty votes asso- claim. However, as long as the value deposit forfeit function satisfies ciated with the pool from the control party, and ending the control the inequality condition in Lemma 1, bidders are better off increasing period. their bids by lowering their surplus claims. But doing so has no impact 2) The entire value deposit and the entire surety deposit are returned on the corresponding value claims and therefore cannot cause compet- to the control party. ing bidders to earn more on each share of their toehold positions by 3) The token deposit is released from the applicable smart contract and overbidding.53 returned to the control party. Nonetheless, there is a strategy analogous to toehold overbidding that can have similar effects under the mechanism: surplus claim under- After a Success Termination, the DAO returns to the default gover- bidding, lowering the surplus claim below the point that causes the best nance state with the former control party holding at least 𝑡 𝑑 𝑞 tokens, business plan of the bidder to break even. The goal is to cause the win- where 𝑞 is the quantity of tokens outstanding when the previous auc- ning bidder to also lower its surplus claim. That smaller surplus claim tion ended at time 𝑇 1 . If the former control party wants to retain control reduces the proportion of 𝑇 token holdings that must be sold to the win- and holds less than 50% of the outstanding tokens at termination, it will ning bidder at 𝑃 and incre 1 ases the corresponding proportion on which need to initiate and win a new basic auction. Otherwise, an open period the 𝑇 token hold 0 ers, including the bidder who engaged in surplus claim begins, during which the control aspects of the auction mechanism do under 1 bidding, can earn the full amount of added token value. not operate. Successful surplus claim underbidding is socially desirable because more social surplus is shifted to the 𝑇 token holders, which results in 4.3. Subsequent auctions 1 a positive investment impact while not affecting the result that the best Subsequent auctions to an initial basic auction are of two types. First, business plan is put into effect. An unsuccessful surplus claim under- any party can initiate a basic auction either prior to the termination of bidding, however, has negative social properties. The winning bidder control from a previous auction or at a time which is not within a control implements an inferior business plan. To the extent of the underbid, ad- period. There is nothing new about a basic auction initiated outside of a ditional apparent social surplus flows to the 𝑇 1 token holders based on control period, but when a basic auction is initiated during a control pe- the value deposit forfeit function, which will result in a positive invest- riod, the DAO Code will need to specify how that auction interacts with ment impact. However, this impact is larger than is optimal, because at the control framework in place following the previous auction. Second, least part of the surplus is apparent rather than real, being in excess of the DAO Code specifies potential periodic auctions. These potential auc- what would be generated even by the best business plan.54It is not clear tions commence when the control period reaches the time limit specified how these two impacts balance out across auctions, but it is clear that a by the DAO Code. net negative effect is possible. 4.3.1. Basic auctions during a control period 4.2. Post-auction operation During a control period, the entire control structure, including a to- ken deposit, a value deposit, and a dynamic vote pool, along with all of the associated parameters, will be embodied in one or more smart In this subsection, we examine post-auction operation absent a sub- contracts. If a party initiates a basic auction during a control period, sequent auction, deferring discussion of subsequent auctions to the next then there are two scenarios: (i) the control party bids in the auction subsection. After the basic auction, the winning bidder is now the con- and wins; (ii) some other party wins the auction, whether or not the trol party because the empty votes held in the dynamic vote pool plus the control party bids. In the first scenario, there will be an Auction Rese t votes associated with the token deposit give the winning bidder more implemented via a set of Auction Reset Steps. These same Auction Reset than a majority of the DAO votes outstanding. Control persists for a con- Steps apply to periodic auctions when the previous control party bids t t t r i h m o e l e p c w o er n h io t e r d o n , l t t h h p e a e r D t t i y A m ’s O e t C p o e o k r e d i n e o d c d l e b o p e se o tw s s i t e t h , e e n v d a t l y h u n e e a e m d n e d i p c o o v f s o i t t t h e , e a p n b o d a o s l s i . c u I n r a e u t t h c y e t i d o m e n p e a a o n n si t d t i m t a h r e e e , a a 𝐷 n n 𝑠 d d , a t w h n i a d n t s 𝑡 t . 𝑑 h S 𝑞 e u . p p D a p e r o a n s m o e t e t e h t e t a h r t s e t f h r c e o o m r n r e e t w s h p e o a p n u r d c e t i v n io i g o n u p b s a e r a g a u i m n ct s e i t o a e n t r s 𝑇 w 𝑐 e e , m 0 re a e n r 𝑆 g d , i n 𝑃 e g n 0 d , f r s 𝐷 o a 𝑣 m t , 𝑇 𝐷 th 𝑐 𝑝 , e 1 , locked in appropriate smart contracts, to be released in part or entirely new auction and the associated winning bid with a superscript “𝑤,” ex- when certain conditions are met. cept that, as stated above, we assume for convenience that the number There are various circumstances under which the DAO Code will of tokens outstanding remains at 𝑞. In this first scenario, as well as sub- end the control period arising from a previous basic auction. One such sequent ones, we will use a reference price 𝑃 𝑟𝑒𝑓 equal to the token price circumstance, discussed in the next subsection, is when there is a later, as of the time 𝑇 𝑐,0 when the auction begins, which we denote 𝑃(𝑇 𝑐,0 ).55 supervening auction. However, there are situations in which the DAO We now develop a transitional forfeit function that determines how Code will end the control period in the absence of a supervening auction. much of the value deposit the control party forfeits when the control We examine one such situation next. A Success Termination occurs if the token price reaches at least 𝑆 on a sustained basis. “Sustained basis” must be defined in a manner that 55 Use of a price at a single point in time to settle value and surety deposits or is code feasible. For example, the criterion might require that the token to set auction parameters creates the danger that various parties will attempt to price, as determined by some group of price oracles maintained by the manipulate market prices at that point of time, perhaps combined with choosing DAO, averages at least 𝑆for 30 days and sustains a value at or above 𝑆 the timing of actions such as initiating an auction or abandoning control. See consecutively for at least 10 of those days. A Success Termination has s le u v p e r l a s F o o f o r t e n sp ot o e n 4 se 5 . a F n ir d s t a , c i c n o s m o p m a e n y ju in ri g s d te ic x t t i o in n s S , e s c u ti c o h n a 4 s . 1 th .4 e . U T n h i e t r e e d a S r t e a a te t s l , e a m s a t r t k w e o t the following consequences: manipulation is illegal and is policed by regulators. Second, the mechanism it- self can choose a reference price that estimates the price on the crucial day but is harder to manipulate, such as using an average of prices during a time interval 53 The result in Lemma 1, that making excessive value claims is a dominated surrounding that day. There are many possible approaches, and avoiding manip- strategy, remains intact. ulation may have costs in terms of accuracy. In addition, in some cases, if capital 54 Investment is over-encouraged if we look at this auction event in isolation. markets are developed enough and active, market forces may constrain manipu- It is possible that the transfer in excess of actual social surplus generated by this lation. For example, engaged and informed short sellers may defeat attempts to type of event offsets the failure to shift the full amount of social surplus to the 𝑇 manipulate prices upward. It is clear that the best mechanism responses to the 1 token holders in other auctions. In short, the transfer in excess of social surplus manipulation danger may depend on trading market quality and the features, may be second-best optimal in some instances. including market liquidity, of particular DAOs. We discuss some of these manip- 15 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 period ends with another auction. Because there are multiple instances We have explained the transitional forfeit function based on the first in which this situation can arise, it is convenient to specify the function scenario for a subsequent auction, the one in which the previous control and explain its operation in advance to avoid tedious repetition. party wins the auction. The same transitional forfeit function applies Define Δ𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃(𝑇 𝑐,0 )), the value deposit forfeit differential, in the second scenario, in which the previous control party loses the which we will use for the case 𝑃(𝑇 𝑐,0 )≥𝑃 0 : subsequent auction. Much of the reasoning for applying this particular ( ) function in the second scenario is the same or analogous, but we leave Δ𝜙= 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃(𝑇 𝑐,0 ))−𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆𝑤,𝑃(𝑇 𝑐,0 )) the details to later. With the transitional forfeit function in hand, we are + ready to state the Auction Reset Steps, the transitional rules that apply where (𝑍) + =max(0,𝑍)is the positive part of the quantity or function in the first scenario. 𝑍. The purpose of this differential is to reduce the value deposit forfeit The Auction Reset Steps are: amount imposed at the end of the initial control period to the extent that the control party has recommitted to honoring the surplus claim, 𝑆, from the first auction.56 The first term is the forfeit amount that 1) The purcha{se deposit. The }control party made a purchase deposit of would be imposed at the end of the initial control period if there were 𝐷 𝑝 𝑤=max 𝑆𝑤 𝑅 − 𝑤 𝑃𝑤 𝑃 0 𝑤,0 as part of the current auction. The ap- no adjustment. The second term is an appropriate credit in terms of the propriate smart co 0 ntract deploys the purchase deposit to buy 𝑡𝑤𝑞 i t n h i a t t i a t l h c e o c n o t n ro tr l o p l e p r a io rt d y v i a s l c u o e m d m ep it o t s in it g fo to r fe a i t t t a f i u n n a c t t io le n a s b t a t s h e e d t o o n k e t n h e v a f l a u c e t tokens at 𝑃 0 𝑤 from the 𝑇 𝑐 𝑤 ,1 token holders pro rata based on th 𝑓 eir b c 𝑆 o e 𝑤 n ca t > r u o s 𝑃 l e ( p f 𝑇 a e 𝑐 i r , l 0 i u o ) r d d e u w t r o i i n l c l g l o r t e s h e s e u t n l h t e e i w n g a c a p o n c b t o e r r t o r w l e p e sp e e n r o i n o 𝑃 d d ( i . 𝑇 n T 𝑐 g , h 0 e l ) o c a s o n s m d o m f 𝑆 p 𝑤 it a m d rt u e n r o i t r n i g a s l c t l h r e o e d f n i t b e h l w e e 2) t T 𝑇 h h 𝑐 𝑤 e , e 1 c t t o o o k n k e t e n r n o d l h e p p o a o l r d s t i i y t n ’ a s g n s t d . o k T d e h y n n e a d D m e A p ic O o v s i o C t t . o e d p e o o a l d t d ra s n t s h it e io p n u . r T c h h e a s t e o d k e t n o k d e e n p s o s t i o t value deposit applicable to that period. shifts from 𝑡 𝑑 𝑞 to 𝑡𝑤 𝑑 𝑞 after appropriate token deposits or with- Define 𝜙∗(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃(𝑇 𝑐,0 )), the transitional forfeit function, as d ap ra p w ro a p ls r ia b t y e t s h m e a c r o t n c t o ro n l t r p a a c r t t y d . u T ri h n e g t t o h k e e n s u d b e s p e o q s u i e t n i t s c re o t n a t i r n o e l d p i e n r i t o h d e . follows: The dynamic vote pool continues in place, adjusting the parameter ⎧ ⎪ Δ𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃(𝑇 𝑐,0 )) if 𝑃(𝑇 𝑐,0 )≥𝑃 0 𝑡 𝑑 to the new value 𝑡𝑤 𝑑 . 𝜙∗=⎨𝐷 𝑣 if 𝑃 0 >𝑆𝑤>𝑃(𝑇 𝑐,0 ) 3) The value deposit transition. When the new auction concludes at time ⎪ ⎩Δ𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃 0 ) if 𝑆𝑤≥𝑃 0 >𝑃(𝑇 𝑐,0 ). v 𝑇 a 𝑐, l 1 u , e t d w e o po c si o t n 𝐷 tr 𝑣 ol a r p i a si r n ty g v fr a o l m ue th d e e p p o r s i i o t r s a a u re c ti o o u n t , s t a a n n d d i a n g cu : r a r e p n r t e v v a io lu u e s We have already described the operation of this function in the first deposit 𝐷 𝑣 𝑤 that the control party made at the time of submitting case, 𝑃(𝑇 𝑐,0 )≥𝑃 0 . In the second and third cases, 𝑃(𝑇 𝑐,0 )<𝑃 0 . The the control party’s final bid in the just completed auction. The cur- fact that the token price outcome was less than 𝑃 0 raises the possibil- rent value deposit is retained. Out of the previous value deposit, the ity of value destruction by the control party. However, the two cases amount forfeited by the control party is 𝜙∗(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃(𝑇 𝑐,0 )), are quite different on this dimension, and, as a consequence, quite the applicable value of the transitional forfeit function. This forfeited different forfeit amounts are appropriate. In the second case, the out- amount is paid to the 𝑇 token holders from the previous auction pro 1 come below 𝑃 0 is not accompanied by any commitment by the control rata based on their 𝑇 1 token holdings. The remainder is returned to party to bring the token value to or above 𝑃 0 during the new con- the control party. trol period. Thus, it is appropriate for that party to suffer full loss of 4) Treatment of the current surety deposit. Parallel to the value deposit, the previous value deposit, including any baseline loss penalty, 𝜙 0 = there are two surety deposits outstanding at the end of the auction: 𝐷 𝑣−(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞, which, as discussed in Section 4.1.1, is useful for a current surety deposit, 𝐷 𝑠 𝑤 , and the previous surety deposit, 𝐷 𝑠. The deterring value destruction. current surety deposit is retained in an appropriate smart contract. In the third case, by making a value claim 𝑆𝑤≥𝑃 0 , the control party 5) Treatment of the previous surety deposit. Define the following three is committing to raising the token price to at least 𝑃 0 during the new shortfall parameters: control period, subject to losing part or all of the new value deposit if the commitment is not fulfilled. The costly commitment to restore the (i) The value shortfall: 𝐻=max{(𝑃 −𝑃𝑤)𝑞,0}. lost value suggests that the control party was not motivated by value de- (ii) The adjusted value shortfall: 𝐻∗= 0 max 0 {𝐻−𝐷 𝑣 ,0}. struction during the initial period. As a result, imposing the baseline loss (iii) The bid shortfall: 𝐵=max{(𝑃 −𝑆𝑤)𝑞,0}. penalty is not appropriate. Instead, the starting point is 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 0 ), 0 a p b a e f n s o e a r d l f t e y o it . n a W r m e e a o s r u o e n n d t i u n e c g q e u s t i a m h l i i s t l o a f r o t r h t f o e e i t v t h a e a l m u fi e r o s u d t n e c t p a o s b e s y i : t , T c r h 𝐷 e e d 𝑣 c , i t o i l n e n s g t s r o 𝜙 t l h ( p 𝐷 e a 𝑣 b r , t a 𝑃 y s 0 e h , l a i 𝑆 n s 𝑤 e c , o l 𝑃 o m 0 ss ) - T a au n h d c e t i D t o r A n a O n p s r C m o o i r d ts a e t t a r h e b e tu a r s r e e n s d s t m o t n o a x t t { h h 𝐷 e e i 𝑠 r 𝑇 − 𝑇 1 𝐵 t t o , o 𝐷 k k e 𝑠 e n − n h 𝐻 h o o l ∗ l d d , e 0 in r } s g t s f o . r o th m e c th on e tr p o r l e v p i a o r u ty s mitted to reaching 𝑆𝑤>𝑃 , making a penalty appropriate only with 1 0 respect to the gap [𝑆𝑤,𝑆], a gap encompassing the portion of the failed As will be discussed more extensively in Section 5.2below, the surety commitment from the initial period that has not been renewed in the deposit is designed to protect against value destruction by bidders who new period.57After subtracting the credit, we arrive at exactly the for- gain control of the DAO. We make some observations for the scenario feit amount Δ𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃 0 )stated above for the third case. we are considering, in which the control party wins the new auction. Loss of part or all of the surety deposit only comes into play if: (i) the value of the DAO has fallen below 𝑃 𝑞 at the time the new auction u po la s t s i i o b n le d r a e n m g e e d rs i e i s n t o S e f c u t t i u o r n e 5 w .7 o , r k b . ut leave a full exploration of the dangers and commences, creating a value shortfall 0 (𝑃 0 −𝑃 0 𝑤)𝑞; and (ii) this value c 5 a 6 lly N d o e te c r t e h a a s t e i i n n m 𝑆 o . s A t l c o a w se e s r , v t a h l e u e fo c r l f a e i i m t a w m il o l u r n e t s u 𝜙 lt ( 𝐷 in 𝑣 , a 𝑃 l 0 o , w 𝑆 e , r 𝑋 fo ) r w fe i i l t l i m f t o h n e o s t a o m ni e - s tw ho o r t n f e a c ll e s i s s a g ry re c a o t n er d i t t h io a n n s t a h r e e m pr e e t v , i i o f u 𝑆 s 𝑤 va ≥ lu 𝑃 e 0 , d t e h p e o e s n it t i 𝐷 re 𝑣 p . r E e v v e io n u s if s u th r e e s ty e token value 𝑋<𝑆is realized by executing the business plan. Thus, the differ- deposit is returned. The control party can therefore block losing any part ence that defines Δ𝜙will be positive if and only if 𝑆𝑤<𝑆. In that case, the control party has not fully reaffirmed the commitment to reach 𝑆, which was embodied in the value deposit 𝐷 𝑣required in the first auction. Thus, some loss posit commitment in the extra range [𝑃(𝑇 𝑐,0 ),𝑃 0 ]given that 𝑃(𝑇 𝑐,0 )<𝑃 0 . This of that previous value deposit is appropriate. extra range was not part of the control party’s original commitment in the first 57 The appropriate level of credit is 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆𝑤,𝑃 0 ), rather than auction, a commitment that only involved values greater than or equal to 𝑃 0 . 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆𝑤,𝑃(𝑇 𝑐,0 )), a larger amount that includes the new value de- The goal is to credit appropriately for settling up that original commitment. 16 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 of the previous surety deposit by bidding at least 𝑃 . However, in the destruction, justifying the return of the entire previous surety deposit. 0 case where there is a value shortfall (𝑃 −𝑃𝑤)𝑞>0, the entire value Second, losing the auction means that the control party loses the op- 0 0 shortfall becomes part of the current value deposit and is at risk. The portunity to bring the token price to 𝑆 or above and thus redeem the potential of loss remains to that extent. previous value claim. At the same time, given 𝑆𝑤≥𝑆, the winning bid- In the second scenario, the control party loses the new auction. The der is asserting that it will be able to do so. And the losing control party’s winning bidder is treated according to the Basic Auction rules with re- value-building efforts or identification of an opportunity may have been spect to all aspects, including deposits, the creation of a dynamic vote part of the basis for the winning bidder’s value claim of at least 𝑆. Un- pool, and the initiation of a new control period. Again, denoting the pa- der these circumstances, withholding the return of any portion of the rameters emerging from the new auction and the associated winning bid previous value claim is not consistent with creating appropriate incen- with a superscript “𝑤,” the losing control party is treated according to tives for bidders who are capable of adding value to the DAO through the following Control Party Auction Loss Steps, which include exactly the their efforts. Similar reasoning justifies the return of part of the previ- same treatment of the previous value and surety deposits as under the ous value deposit as specified by the transitional forfeit function when Auction Reset Steps, the applicable transition rules for the first scenario: 𝑆𝑤<𝑆 but 𝑆𝑤≥𝑃 . 0 Finally, note that the portions of the value deposit and surety deposit 1) Closing the previous dynamic vote pool. The previous dynamic vote that are not returned to the losing control party are remitted to the 𝑇 1 pool is closed, removing all the empty votes associated with the token holders from the previous auction, regardless of whether or not pool from the losing control party, and ending the control period they have retained their 𝑇 token holdings. The potential return of the 1 associated with that party. deposits attaches to the holders and not to the tokens. As a result, poten- 2) Return of the previous token deposit. The previously existing token tial return of the deposits does not affect the market value of the tokens. deposit is released from the applicable smart contract and returned Otherwise, buyers would price in the probability of deposit returns, in- to the losing control party. creasing the value of the tokens above the level that would follow from 3) Treatment of the previous value deposit. The losing control party for- future business prospects alone. This kind of distortion would be prob- feits 𝜙∗(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑆𝑤,𝑃(𝑇 𝑐,0 )) of the previous value deposit, the lematic because the auction mechanism relies on the token price being amount specified by the transitional forfeit function. The forfeited a meaningful signal of the value of the DAO. amount is paid to the 𝑇 token holders from the previous auction pro The control party may want to relinquish control in the absence of a 1 rata based on their 𝑇 token holdings. The remainder is returned to supervening auction by Abandonment. In this scenario, the Control Party 1 the losing control party. Auction Loss Steps apply, setting 𝑆𝑤=𝑃𝑤 , as if the control party lost 0 4) Treatment of the previous surety deposit. Define the following three the auction to a bid that included a value claim equal to the current shortfall parameters: market value at the time of Abandonment. (i) The value shortfall: 𝐻=max{(𝑃 0 −𝑃 0 𝑤)𝑞,0}. 4.3.2. Periodic auctions (ii) The adjusted value shortfall: 𝐻∗=max{𝐻−𝐷 𝑣 ,0}. If the entire control period elapses without early termination due to (iii) The bid shortfall: 𝐵=max{(𝑃 0 −𝑆𝑤)𝑞,0}. success or a supervening auction, then the DAO Code triggers a new basic auction. The new auction starts at the end of the control period, T a au n h d c e t i D t o r A n a O n p s r C m o o i r d ts a e t t a r h e b e tu a r s r e e n s d s t m o t n o a x t t { h h 𝐷 e e i 𝑠 r 𝑇 − 𝑇 1 1 𝐵 t t o , o 𝐷 k k e 𝑠 e n − n h 𝐻 h o o l ∗ l d d , e 0 in r } s g t s f o . r o th m e c th on e tr p o r l e v p i a o r u ty s a 𝑃 n 0 𝑝 d , I f a t h s t h e o e f p r t a e h r a a is t m a t e i t m t e le e r a . 𝑃 st 0 o is n e se b t i a d t d t e h r e , t v h a e lu n e t h o e f t a h p e p D ro A a O ch g e o s v o e f r n th a e n c p e r e to v k io e u n s , subsection apply directly. If the control party wins, the DAO Code im- Several features of these rules are noteworthy with respect to their plements the Auction Reset Steps. If the control party loses or does not role in creating participant incentives through the auction mechanism. bid, then the Control Party Auction Loss Steps apply. If no one bids, then First, in the normal situation in which 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑋)is monotonically the control party is treated as losing an auction in which the winning d lo e w cr e e r a p si o n t g e n i t n ia 𝑋 l va ∈ lu [ e 𝑃 0 d , e 𝑆 p ] o , s i t t h f e o r l f o e s i i t n a g m c o o u n n tr t o t l o p t a h r e t y e x i t s e n re t w th a e r d o e u d t c b o y m a e b ap id p l i y n , c t l a u k d i e n d g a 𝑆 v 𝑤 al = ue 𝑃 c 𝑝 la a i n m d 𝑃 of 𝑤 𝑃 = 0 𝑝 : 𝑃 T 𝑝 h i e n C te o r n m tr s o o l f P t a h r e ty n A ot u a c t t i i o o n n u L s o e s d s i S n t e th p e s 𝑃(𝑇 𝑐,0 ) that the party delivers as of the beginning of the subsequent Steps. 0 0 0 auction is higher. Second, if the winning bid in the subsequent auction It is worth considering some situations in which a periodic auction includes a value claim of 𝑆or higher, then the losing control party is off is triggered by the passage of time. Suppose that the control party is still the hook.58 Similarly, if the losing control party’s bid includes a value confident of attaining a sustained token price of 𝑉∗as the business plan claim of at least 𝑆, in effect renewing a commitment for the DAO to- plays out. The fact that a periodic auction is taking place means that to ken to reach this level, then unless opposing bidders can win with a bid date, only a lower sustained level has been attained. In this situation, the below 𝑆 because they have significantly lower costs, the control party control party has a strong incentive to bid in the periodic auction with will not lose any of the value deposit. the bid including a renewal of the previous value claim, so that 𝑆𝑝= As noted, the treatment of the previous surety deposit is exactly the 𝑆=𝑉∗, where 𝑆𝑝 is the new value claim applicable to this particular same as in the scenario in which the control party wins the auction and periodic auction. This bid means that the control party will not lose any the Auction Reset Steps apply. We add some observations with respect to part of the previous value or surety deposits. That will also be the case losing control parties, leaving a comprehensive discussion of the surety if another bidder wins with an even higher value claim. deposit for later in Section 5.2. A winning bid with a sufficiently high A second situation is where the control party engaged in extreme value claim will guarantee the return of the previous surety deposit, the value destruction, dropping the initial token value from 𝑃 to some small previous value deposit, or both. In particular, 𝑆𝑤≥𝑃 0 results in a re- but nonzero value. If no one, including the control party 0 , bids, then in turn of the previous surety deposit, and 𝑆𝑤≥𝑆 guarantees the return the standard case, the control party will lose 𝑃 𝑞. The control party 0 of the entire previous value deposit. The return of these deposits under can forestall loss of both the value deposit and the surety deposit by the applicable conditions is justified by the following reasoning. First, submitting a new bid that renews the previous value claim.59 Given the condition 𝑆𝑤≥𝑃 based on a value claim by an independent bid- 0 der suggests that the control party did not engage in significant value 59 The value deposit from the previous auction is returned to the control party because the new value claim is at least as high as the value claim from the 58 See Footnote 56supra. previous auction. The surety deposit from the previous auction is returned to 17

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 that the DAO has nominal value, it is a near certainty that there will to expect other common knowledge elements to be present and avail- be no competing bids. But unless the control party puts resources and able to the mechanism, especially because essential elements such as effort into the DAO, the low value will persist until the next periodic the bidding participants and the surrounding circumstances may not be auction. In effect, the value and surety deposits will be stuck in the DAO known until shortly before or during the auction itself. and effectively lost.60 A more profitable strategy for the control party The problem of extracting surplus is equivalent to designing a rev- is to allow its control to expire, whether or not there is a bidder in the enue maximizing auction. Here, the “revenue” is the added token value periodic auction, thereby releasing its entire remaining token deposit, that remains from the business plan after subtracting the amount of which the control party can sell to at least recover some money. In fact, added token value, 𝑅+Π𝑡𝑏 , that accrues to the winning bidder. We the control party may want to abandon the control position before even have used an English auction, which is a second-price auction because reaching a periodic auction. Abandonment has the same consequences the winning bidder pays the amount of the second highest bid. Various because the same Control Party Auction Loss Steps apply that pertain to other auction types may raise more revenue under particular circum- loss of a periodic auction in the case where there are no bidders in that stances. For example, if bidders are risk averse, a first-price auction will auction. raise more revenue but may also result in an inefficient outcome, which in our case means that the business plan creating the most social sur- 5. Further evaluation of the mechanism plus may not be selected. Furthermore, adding some additional realistic assumptions, such as bidders whose outcome possibilities differ because 5.1. Impact on investment of different levels of skill, makes it unclear whether a first-price auction indeed would raise more revenue than an English auction. As discussed in Section 3, an important consideration is the impact of Another consideration is that sealed-bid first-price auctions may the sequential auction mechanism on initial investment in DAO projects. avoid the collusion problems that can arise in second-price auctions. The first best is to offer winning bidders only the amount of added token Collusion coalition parties in a sealed-bid first-price auction can defect value required to cover their costs and execute their business plans. If by bidding above an agreed-upon low price chosen to enable the highest initial investors expect that they will retain more social surplus in sub- valuing bidder to prevail at that price and thus collect the largest pos- sequent auctions, they will pay more for the venture in the first place. sible amount of added token value for the coalition. In a second-price A mechanism with the highest expected retained social surplus will re- auction, the highest valuing bidder will submit their best bid, and other sult in the highest possible funding for the DAO at the start-up point, as coalition members cannot win the auction by deviating. Deviating only well as the highest possible ongoing investment value. reduces the joint added token value for the coalition. The potential con- One question is whether full surplus extraction (FSE) is possible. At siderations in choosing among auction forms are myriad, and we do not present, it appears that FSE is attainable only under prescribed, rela- attempt a detailed discussion here.62Instead, we simply rest on a claim tively narrow conditions. In particular, Crémer and McLean [47]showed that, given current knowledge, the English auction is a strong candi- that if types are a finite set, the types are correlated, the joint probabil- date with respect to efficiency and raising revenue compared to other ity distribution of types is known to both the mechanism designer and standard auctions.63 the bidders, and that probability distribution meets certain conditions, An English auction has other strong traits worth mentioning. An En- then it is possible to design an FSE mechanism. A large literature sur- glish auction is “obviously strategy proof” in the sense of Li [50]. In rounds and extends this result, encompassing, for instance, a continuum intuitive terms, it is an obvious dominant strategy to bid until one’s true of types, applicable here because 𝑉∗and 𝐶∗are real numbers.61 value is reached and then drop out, at least when there is a continuum These possibility results are almost certainly not relevant here. The of bidder types.64This quality minimizes the possibility that the auction assumption that the joint probability distribution of types is known to will go awry due to the inability of some subset of bidders to understand both the mechanism designer and the bidders is highly implausible. Fu what they should do under the mechanism.65 et al. [48]showed that sampling without prior knowledge from this dis- Another feature that relates to surplus extraction is the reserve price. tribution may suffice to achieve FSE, but it is unclear how that sampling The mechanism requires 𝑆≥𝑃 0 , setting a reserve price equal to the to- ken price at 𝑇 , the start of the auction period. This reserve price makes could occur in the context here. 0 market dynamics and market efficiency important. Token holders antic- Robert Wilson’s statement of the so-called “Wilson doctrine” in ipate that the DAO project might be improved in the future, and an Ref. [49] is particularly apt in the context of designing mechanisms for DAOs: 62 A good starting point is Krishna [34]. Game theory has a great advantage in explicitly analyzing the conse- 63 We have been assuming a “private values” setting with asymmetric informa- quences of trading rules that presumably are really common knowl- tion in which bidder business plans are known only to each bidder and bidder edge; it is deficient to the extent it assumes other features to be com- valuations of the plans are independent. See note 39supra. If, instead, there is mon knowledge, such as one agent’s probability assessment about a common values element in which bidders have different signals concerning another’s preferences or information. I foresee the progress of game the value of the current operation and bid based on perceived undervaluation theory as depending on successive reductions in the base of common at price 𝑃 0 , then the efficiency and surplus-distribution of various auction meth- knowledge required to conduct useful analyses of practical problems. ods are potentially different than under the private values assumption. However, Only by repeated weakening of common knowledge assumptions will the English auction performs relatively well in a common values setting. Under the theory approximate reality. c re e m rta a i i n n s a e ss ffi um cie p n ti t o i n n s t s h u e c h se a n s s e th t e h a a t v t e h ra e g re e i c s r o a s n s i e n x g - p p o r s o t p e e q r u ty il , i b th r e iu E m n g in li s w h h a i u ch ct i t o h n e bidder who can add the most value will win [34, pp. 134–143]. In this set- Trading rules are code feasible, and reducing them to code makes them ting, the English auction tends to raise more revenue than other approaches, common knowledge among all potential bidders. But it is unreasonable including sealed-bid first price and second-price auctions [34, pp. 97–100]. In the context here, raising more revenue equates to extracting more added token value from the winning bidder, one of our desiderata. the control party because the bid shortfall is zero. But the value deposit for the 64 As discussed in Section 4.1.6, when there is not such a continuum and es- new auction equals or exceeds the sum of the previous two deposits. pecially when there is a small number of bidders, there may be an incentive to 60 The DAO Code could create a maximum number of sole-bid control periods overbid. to close out the stuck position, but this might entangle honest control parties 65 On a similar note, Neeman [51]demonstrated the robustness of the English with projects that take a long time to prove out. auction to the seller’s degree of “Bayesian sophistication” with respect to setting 61 Borgers [15, pp. 120–128]contains a good general discussion. a reserve price in particular private-values environments. 18 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 efficient token market implies capitalization of these expectations in there will be no problem if the control party remains confident in the the form of a higher token price. To the extent that the expectations business plan. In that case, the control party will reinstate the previous are cogent, the auction will involve much less social surplus. In effect, bid, which includes a value claim 𝑆>𝑃 , ensuring the return of the 0 some social surplus was already extracted and accrued to the investors entire surety deposit. On the other hand, if the control party no longer through the impact of the capitalized expectations. If the expectations has enough confidence in the business plan to bid with a value claim err to the high side, the token will be overvalued, potentially blocking of at least 𝑃 0 , a bid that would trigger the return of the entire surety implementation of even the highest social surplus business plan. How- deposit, then there is a loss. But this loss is appropriate because it is ever, when no innovations emerge after a period of time, it is likely that due to the failure of the business plan, a failure that drove the expected the token price will fall until an innovation becomes feasible under the token price below the original starting value, 𝑃 0 .68 auction mechanism. It is not clear how prevalent and potent these phe- By choosing the parameter 𝛾≤1, it is possible to calibrate the surety nomena might be, but it is clear that they might have a big impact on deposit appropriately to the level of threat posed from potential value surplus extraction and thus on initial investment.66 destruction by a control party. In particular, 𝛾 can be set to a value consistent with the operating and financial environment of the DAO. 5.2. Preventing value destruction We have seen that if 𝛾=0is chosen, then between the surety deposit and the value deposit, a control party engaging in value destruction risks The danger of value destruction arises from the possibility that the forfeiting up to 𝑃 0 𝑞, the entire pre-auction value of the DAO, through control party will take the equivalent of a negative economic position loss of the surety and value deposits. Circumstances may dictate that 𝛾 in the DAO, one that would increase in value if the DAO flounders, and does not need to be that low. For example, if value destruction is time- then will use control to cause the DAO to perform poorly or even to fail consuming, and there are many potential, informed bidders available to e to n k ti e r n e s l y w . o T u h l e d v d a e l c u l e in o e f i t n h t e h c e o e n v t e ro n l t p o a f r v t a y l ’ u s e t o d k e e s n tr d u e ct p i o o s n i , t b c u o t n t s h is e t i d n e g t e o r f r e 𝑡 𝑑 n 𝑞 t s lo te s p s t i o n , t h t e h e c n o n it t r i o s l l p ik a e rt l y y , t b h y a t a v n a e l w ue a d u e c s t t io ru n c . tion will be prevented, at a effect of this deposit is not EV-robust. The control party can remove the The design of the value deposit and its interrelationship with the economic aspect of this position, converting the position to empty votes, surety deposit are important considerations with respect to value de- through a variety of empty voting strategies. As pointed out in Section struction. Because value destruction necessarily involves driving the 2.2, some of these strategies are not costly and would be hard to detect token value below the baseline price, 𝑃 0 , a party intent on value de- by any available means, much less by code feasible methods. The rest struction will forfeit the entire value deposit for certain. A larger value of the control party’s votes are from the dynamic vote pool, and these deposit is a stronger deterrent against value destruction. votes are empty votes by design.67Thus, the control party can arrange Increasing the value deposit may have undesirable collateral con- to secure control entirely through empty votes. sequences. In particular, as discussed more fully in Section 5.4, there Both the value deposit and surety deposit are at risk if the control is a danger of creating excessive and socially counterproductive post- party engages in value destruction. Although the value deposit also plays auction incentives for control parties to expend costly effort aimed at a role in eliciting bids and incentivizing post-auction performance, the increasing the value of the DAO. It is here that the baseline loss penalty described in Section 4.1.1 is particularly valuable. That penalty is a sole purpose of the surety deposit is to supplement the value deposit in fixed amount that is levied if and only if the token price outcome is order to deter value destruction. Recall that the surety deposit is: less than 𝑃 . As discussed in Sections 4.1.1and 5.4, this penalty can ac- { } 0 𝑇 𝑠=max 𝑃 0 𝑞(1−𝛾)−𝐷 𝑣 ,0 c d o e m sig p n a e n r y t t h h e e f r s e ta e n d d o a m rd t o v a m lu o e ld d t e h p e o s fo it r f f e o i r t f e a i m t o fu u n n c t t s i o fo n r , o w u h t i c c o h m a e l s lo g w re s a t t h e e r where 𝛾is a choice parameter and 𝐷 𝑣is the value deposit. If 𝛾=0, then than or equal to 𝑃 0 in any way desired to achieve the best possible set the surety deposit is set such that the sum of the surety deposit and the of post-auction performance incentives. The baseline loss penalty will value deposit is 𝑃 0 𝑞, the entire value of the DAO at the beginning of the deter value destruction of any magnitude, no matter how small, and in- auction. If the control party engages in value destruction that drives the creasing it does not affect the post-auction performance incentives of value of the DAO to 0, then the control party will forfeit both deposits in parties not intent on value destruction. their entirety. Loss of these deposits is EV-robust. As discussed in Section Finally, note that if deterrence fails and value destruction is success- 5.4, the control party would have to pay substantial sums to construct ful, forfeiture of the deposits fully compensates the token holders other a derivative position that covered the loss of both deposits. than the control party. They are in at least as good a position as they The surety deposit is useful in deterring potential value destruction, would be if the claimed business plan had been executed successfully. but it also may deter bidders who intend to create value. Despite being confident that their business plans will move the DAO value up from 𝑃 𝑞 5.3. Undervaluation and treasury raid scenarios 0 to 𝑆𝑞, there may be an interlude in which the DAO governance token price falls below 𝑃 before the business plan proves itself. An auction Potential “treasury raid” scenarios provide an interesting perspective 0 during that interlude, including a periodic auction if the control period on how the mechanism would operate. DAOs typically have treasuries ends during the interlude, creates the danger of loss of part or all of the consisting of cryptocurrency tokens that can be used for further devel- surety deposit under the applicable Auction Reset Rules or Control Party opment of the DAO. Treasuries can store retained earnings as well as Auction Loss Rules. In the deterministic setting we have been assuming, funds received from investors. Treasuries may be under the direct con- trol of token holders who can direct their use by voting on proposals.69 Direct control by token holders creates the danger of “treasury raids.” 66 One possibility is to create a multiple-stage model, such as the one in Ordóñez-Calafi and Bernhardt [52], with the initial investments in the DAO oc- curring at the first stage and auctions at later stages. This type of model would 68 In the assumed deterministic setting, only auction-initiated business plans permit examining the impact of the degree of surplus extraction in the auctions and the timing and degree of their success determine token prices. Low token on initial investment and how that impact depends on various parameters. We price outcomes may occur due to stochastic elements not associated with the leave the development of such a model or analogous ones to future work. cogency of the business plan. As discussed in Appendix A.2, an appropriate re- 67 The creation of empty votes through a dynamic vote pool is extremely useful. sponse to that possibility is particular ex ante adjustments to each of the deposits It allows the winning bidder to secure control with less than a majority of the as well as to the value deposit forfeit function. tokens, thereby enabling the 𝑇 token holders to secure a greater proportion of 69 In some cases, there are other parties who have that formal power or a 1 the social surplus generated by the bidder, which will have a positive investment veto on token holder proposals for spending treasury resources. In one com- impact. mon organizational structure, the DAO is embodied as a Swiss Foundation. The 19 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 The most pernicious example of a treasury raid is one in which a party that the winning bid will be close to 𝑃 and that most of the so- treasury gains control of the DAO and then transfers the entire treasury to it- cial surplus will flow to the existing token holders.71 Therefore, it is self by voting positively on a suitable proposal. The party is stealing the unlikely that the token value will be significantly underwater, and the other token holders’ stakes, and the term “raid,” along with its negative situation in which the guiding parties are engaging in foolish projects connotations, is apt. will be terminated by the liquidation of the DAO. Other cases and situations are not so clear. A relevant parameter is If, instead, the token value was underwater because the guiding par- whether the token market capitalization is above or below the value ties have a superior business plan that requires secrecy, capital market of the treasury. The “underwater” situation in which the market capi- adequacy means that these parties can obtain funding in confidence to talization is substantially below the value of the treasury is consistent outbid other parties intent on liquidation. The other token holders re- with multiple, contradictory possible realities, each of which calls for a ceive at least their pro rata share of the treasury and possibly also some different perspective and optimal response. We consider three possible of the social surplus from the envisioned superior business plan. If the realities that illustrate challenges for the mechanism in addition to the guiding parties think that they have a superior business plan but can- case of a direct raid on the treasury. These three realities and the direct not convince any funding party of that opinion, then upon liquidation, raid possibility can occur whether or not token prices are underwater, the guiding parties at least receive their share of the treasury, possibly but starting with the underwater case makes the challenges clearer. amounting to enough to implement their business plan through a new First, there may be an expectation that the parties currently guid- project.72 ing the DAO, although good-intentioned, will engage in foolish business The mechanism provides a corrective to the diversion situation. A plans, gradually wasting the treasury assets. The foolish business plans bidder can initiate an auction based on a “business plan” consisting of may be the result of the exhaustion of the original guiding purposes of carrying out the DAO operations without the diversions. This business the DAO. In this case, the social optimum is to end the DAO and dis- plan will increase the token value of the DAO, creating room for the tribute the treasury to the token holders, permitting re-investment of bidder to profit. At least some of the added token value will flow to the the treasury assets in more promising projects. In a situation of capital other token holders. market adequacy, there will be “vulture investors,” who facilitate this Finally, the mechanism will tend to cause the aggregate token value result via a takeover or through activism in the face of reluctant guiding to equal or exceed the value of the treasury. As a result, a treasury raid or control parties.70 executed by using the mechanism to gain control will not be profitable. Second, the guiding parties might have a very promising business The DAO value will fall by an amount that at least approximates the plan but are keeping it secret from competitors. Current operations that missing treasury assets, and the winning bidder will lose that degree of lay the groundwork for that business plan may appear substandard to its deposits, with the lost deposits flowing to the other token holders, market participants, resulting in a market capitalization less than the reversing the stealing inherent in the treasury raid. value of the treasury. In this case, the socially optimal outcome is for the guiding parties to continue in control until the business plan can 5.4. Post-auction incentives and EV-robustness play out and reveal its superiority. Third, the guiding parties may not be totally good-intentioned and At the end of the auction, ignoring any additional token or token- may be diverting treasury assets to themselves short of an explicit dis- derivative positions taken during the auction period, the winning bid- tribution of the entire treasury that could be characterized as a single der, now the control party, holds 𝑡 𝑑 𝑞tokens on which that party hopes “raid” incident. Some of the diversions may be ambiguous or subtle, such to earn added token value and faces the task of avoiding loss of part or as overpaying DAO contractors that are related to the guiding parties. all of the value deposit by executing the business plan in order to move Significant diversions might cause the DAO to underperform noticeably, the token price up to 𝑉∗, the target price. The control party’s incentives resulting in an underwater token price. Diversions are tricky from a to execute this task depend on the value deposit forfeit function and the social optimality perspective. The diverted assets are not lost, only re- party’s actual token position. distributed. Furthermore, if the diversions are anticipated at the time Under the standard token deposit forfeit function and assuming that of investment, investors can give the guiding parties a lower stake for holding 𝑡 𝑑 𝑞 tokens is the control party’s net position, a one-dollar in- the same amount of funding, nullifying the impact of the diversions on crease in the token price will result in a 𝑡 𝑑 𝑞dollar increase in the token investor returns. holdings and a (1−𝑡 𝑑)𝑞 drop in the value deposit obligation. The net Assuming capital market adequacy, the mechanism can address all of result is that the control party is better off by 𝑞dollars for every dollar these situations effectively. Suppose first that the token value is under- increase in the DAO’s token value, which is exactly the increase in the water. Then a bidder can initiate an auction at just above the current to- value of the DAO. In this case, the control party has exactly the correct ken value, 𝑃 0 , when the value per token of the treasury is 𝑃 treasury >𝑃 0 . incentives to put effort into the project because the control party will If the bidder wins, the bidder can terminate the DAO and distribute the capture 100% of the gains and suffer 100% of the losses from taking or treasury pro rata to the token holders. Capital market adequacy ensures 71 The “business plan” of liquidating and distributing the treasury and hedging Foundation acts as a wrapper, creating legal personhood for the DAO, with con- the treasury value over the required short interval of time is unlikely to have comitant limited liability. Under Swiss law, the Foundation must have formal high costs, and because the situation is so clear, it is likely that there will be legal control over the DAO treasury. Although the Foundation may in practice many potential bidders and that most of the potential gain will be bid away, typically defer to token holder votes, there is the power to veto vote outcomes accruing to the existing token holders instead. Bidder deposits will be effectively if they involve disbursing treasury funds. collateralized by the value of the treasury. 70 Vulture investors already exist in the cryptocurrency space. The saga of Rook 72 The outcome in the Rook DAO events described in Footnote 70supra ap- DAO, recounted by Gilbert [53]and Nelson [54], is an example. Rook DAO en- pears to represent these kinds of splits between parties intent on implementing countered an internal conflict and was trading below the value of its treasury. a business plan and parties who want to exit through a liquidation that brings Co-founders and members of the core team proposed shifting 75% of the tokens the DAO value up to the level of the treasury. The Rook DAO treasury assets to themselves to continue the project, leaving 25% to the rest of the token com- were divided between two such groups of parties. The bidding competition cen- munity. Activist investors facilitated an increase in the community’s share to tral to the mechanism creates a way to divide the treasury assets more cogently, 60%. Liu [55]detailed the claimed role of Arca, one of the activist investors. As with the key question being whether the parties who want to continue can out- described in Arca [56]and Dorman [57], Arca’s operations included some that bid the liquidation value. If they can, the other parties receive at least the pro resembled a hedge fund that both makes portfolio investments and engages in rata treasury value of their tokens and likely more. If they cannot, they receive activism. their share of the treasury and can pursue the project with those funds. 20

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 refraining from effort. There is no Jensen-Meckling problem. The con- 5.5. Code feasibility trol party will behave as if it is a 100% owner, comparing the costs of effort to 100% of the potential gains. The auction mechanism is code feasible by design. Deposits take the Nearly costless hedging equivalent to a temporary sale of part or place of derivatives that would require counterparties. The mechanism all of the toehold may be available through the use of derivatives or itself is an easy-to-code algorithm. otherwise. In the case of a control party intent on the business plan Many DAOs contain structural governance limitations that specify and on increasing token value to the target price, any such hedging will which DAO Code or DAO operation changes can be achieved by a ma- have the undesirable consequence of reducing the amount of token gain jority vote, and which changes are subject to more stringent procedures. that the control party will capture. For control parties intent on value Control parties face the same governance restrictions as other parties. destruction, the opposite is the case. Hedging avoids any loss on the Winning an auction only guarantees that a control party can prevail with toehold as a result of the value reduction, and giving away the upside respect to any issue that is subject to a majority vote (>50%), even if the in a hedge is costless for such a party. A hedge equivalent to a sale sets control party holds less than half the tokens eligible to vote. If a higher up an empty voting position, exactly what the control party intent on voting percentage is required, the control party can only succeed uni- value destruction desires. laterally through actual token ownership, as is the case with all other It is clear that no arrangement is going to be EV-robust with respect parties.75 to token holdings. It is easy enough to hedge them in a way that is There is a strong argument for making the code governing the auc- equivalent to a sale. But the same cannot be said of the value deposit tion rules themselves immutable or nearly so.76 As long as this code and security deposit, which are key deterrents to value destruction and is intact, auctions remain as a powerful tool to address governance is- simultaneously incentivize achievement of the business plan. These de- sues and to overturn any hold on the DAO by pernicious control parties, posits are EV-robust. Hedging the value deposit requires purchasing the whether or not the control originated from a previous auction. In ad- opposite derivatives position, which in the case of the standard value dition, the immutability of the auction provisions prevents incumbents deposit forfeit function effectively means buying a put with a 𝑉∗strike from distorting the auction process to their advantage by making con- price and selling a put with a 𝑃 strike price.73 This position would be trol shifts via the auction more difficult or by creating rules that favor 0 expensive in the sense that it would cost a significant proportion of the incumbent bidders. deposit. With respect to outcomes below 𝑃 , a large put position with The biggest difficulty regarding code feasibility is the task of bolster- 0 appropriate strike prices would be required to offset potential forfeits ing toehold reporting discussed in Section 4.1.4 above. It is not clear involving both the value deposit and surety deposit. This put position that detecting failures in toehold reporting is amenable to simple code would also be costly and possibly difficult to assemble without moving solutions. Possible measures include recourse to outside parties, such the token price significantly downward while assembling the position. as bounty hunters, or implementation of a suitable registration system A major advantage of the mechanism is that the control itself is requiring know-your-customer verification. Perhaps the most powerful completely EV-robust. Contesting parties can only succeed by being the approach is to build a flush sale into the mechanism that includes a reg- highest bidder in the auction enabled by the mechanism. Holding or istration system that directs added token value from concealed control assembling empty votes has no impact. The arbitrariness that can be party positions away from the control party. But all of these approaches associated with empty voting cannot occur. require interactions with the outside world and some level of trust that There are factors that might induce a control party intent on suc- goes beyond secure code. cessful implementation of a business plan to hedge part or all of its token position despite the loss of token gain that would flow from 5.6. Decentralization, regulation, and legal aspects success. If the DAO position is a large part of the control party’s portfo- lio, optimal portfolio management may require reducing the long po- A major question is the relationship of the mechanism presented here sition in the DAO. Any such reduction would mean that the control to decentralization, a desideratum for DAOs. This question also has sig- party is under-incentivized with respect to effort. Such a party bears nificant legal and regulatory implications. The auction mechanism is a 100% of the cost of effort but reaps less than 100% of any gains there- control device, creating the possibility of temporary contestable control from. If control parties hedge part or all of their token holdings in the by a single party, which itself may be an entity or group of persons. DAO, there is a case for going beyond the standard token deposit for- That may appear to be a move toward centralization, but arguably it feit function by making the value deposit forfeit amounts larger than is the opposite. As mentioned, many DAOs appear to be under the de 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑋)≊(1−𝑡 𝑑)(𝑆−𝑋)𝑞for each outcome 𝑋. For completely facto control of a relatively small group of active token holders, often hedged control parties, full performance incentives are attainable by connected to the founders, surrounded by a mass of other token holders setting 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑋)=(𝑆−𝑋)𝑞. Then the control party is put in a who rationally do not participate in governance.77 Even if that control position of a 100% owner facing at least the full losses and gains for the shifts, the shifts will be subject to the vagaries of voting procedures and DAO through the value deposit mechanism, which the control party can- empty voting. not evade by hedging. However, if this token deposit forfeit function is The mechanism improves on that situation by making control transi- imposed, then control parties who hedge less than their full token posi- tions more effective, not the result of voting procedures that are subject tion in the DAO will be over-incentivized to perform, creating the danger to social choice flaws, and also not subject to the arbitrariness that can that they will expend costs that exceed the corresponding increases in the value of the DAO.74 75 Careful consideration is required with respect to whether the control party can count its empty votes from the dynamic voting pool as eligible token votes 73 See Footnote 31supra. with respect to issues that require a supermajority vote to resolve. The answer 74 For convenience of exposition, we have gone beyond the deterministic model to this question may depend heavily on which issues are involved and also upon to consider the impact of control party hedging at this point. Appendix A.2 the overall governance structure and philosophy of the particular DAO. discusses hedging strategies more generally and distinguishes between different 76 If the auction provisions are immutable, it will be impossible to improve the types of control parties. If the control party is a large institutional investor or is auction process itself, a move that potentially would increase the value of the funded by one, hedging the DAO token position may be less urgent with respect DAO. If some flexibility is permitted, the danger of possible manipulation sug- to portfolio balancing and may not be worth the potential loss of gains on the gests creating a substantial barrier to revision, such as a very high supermajority tokens. Choosing the form of the value deposit forfeit function and other aspects vote, possibly combined with deposits or other vehicles that shift the risk of any of the DAO may depend heavily on the nature of the particular DAO, including loss in DAO value upon the proposing parties. the characteristics of the likely control parties. 77 See Footnote 3and accompanying text supra. 21 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 arise from empty voting. Most importantly, control is continuously con- is H.R. 4763, a recent bill passed by the U.S. House of Representatives testable. Any party can initiate an auction. Even a majority token holder that would create a comprehensive regulatory framework for cryptocur- cannot maintain control in the face of an auction except by being the rencies.82 This legislation would grant the CFTC primary jurisdiction highest bidder. That is a very different picture from a DAO with en- over any blockchain network or application that is functional and decen- trenched control held implicitly or explicitly by founders or large token tralized.83If the system is not yet functional or is not decentralized, then holders. It is also important to keep in mind that the mechanism creates it is regulated by the SEC. SEC regulation is much more onerous because the possibility of alternation between control periods and open periods it requires formal registration of the project, along with periodic report- in which the DAO reverts to a less organized mode of operation, in- ing requirements. In contrast, unless the project is an exchange, CFTC cluding voting approaches that may be valued for reasons other than regulation is largely limited to addressing fraud and market manipula- promoting operational efficiency. tion. There are no registration or reporting requirements. This difference Regulation of DAOs is not fully defined or developed, and there often is critical for DAOs because DAOs lack centralized management, and, as is considerable uncertainty, especially in the United States, where three a result, compliance with registration and reporting requirements will quite different major regulatory approaches are possible even for the be difficult if it is possible at all. near future. Because these same three regulatory approaches are the The second kind of regulation can be described as a joint and several major candidates across jurisdictions, we consider the mechanism in responsibility approach. Some party or set of parties must be responsible light of each of them. We present multiple examples of the approaches, for meeting traditional regulatory requirements, and in the absence of a but, to create a more enduring discussion in light of the unsettled nature designated party or parties, a wide variety of participants are effectively of cryptocurrency regulation, we focus on the approaches in general at risk of being held responsible with ensuing penalties or liabilities for rather than on specific current instances.78 the failure of the DAO to comply. There is a danger that this approach After introducing and discussing the three regulatory approaches, would preclude decentralized operation entirely. In the United States, we turn to the interaction of the mechanism with regulation. We begin recent developments with respect to both the SEC and CFTC rules gov- with the most important and general point, that by providing additional erning exchanges are striking examples. protection for investors, adding the mechanism greatly strengthens the In a case involving Ooki DAO,84 a commodities exchange operated case for a much less burdensome regulatory regime, which at the same through a DAO, the CFTC claimed that Ooki DAO was an exchange that time is likely to be more effective. Following that general discussion, we was required to register under the Commodities Exchange Act and be consider ways in which the mechanism interacts with existing regulation subject to regulation by the CFTC, but had failed to do so. The founders under the three approaches. had switched the exchange from operating as a limited liability company (LLC) to a DAO, publicly stating that the purpose was to avoid regula- 5.6.1. Three regulatory approaches tion. After settling with the founders, the CFTC proceeded against the The first approach is decentralization-focused in the sense that the de- DAO itself despite the lack of identifiable parties managing the DAO, gree of decentralization determines whether and to what extent DAOs with the result being a default judgment for money damages in excess and other cryptocurrency applications are regulated. There are many of $600,000, an injunction, and an order requiring that Ooki DAO end its variants that fall into this category. Under the recently implemented internet presence [62]. The CFTC took the position that Ooki DAO was European Union laws governing cryptocurrencies, the key role of de- comprised of token holders who had voted on any proposal, whether or centralization is explicit, with an exemption from regulation for the case not related to any regulatory matter. Because Ooki DAO is an unincor- in which “crypto-asset services ... are provided in a fully decentralized porated association, these token holders most likely will be jointly and manner without any intermediary” [58, Directive (22)]. In the United severally liable for the full amount of the money damages. States, the test set forth by the Supreme Court in SEC v. W.J. Howey Co.79 On the SEC side, developments during the 2023–2024 period were determines which cryptocurrencies will be considered “securities,” sub- even more threatening. The SEC reopened the comment period for pro- ject to registration with the Securities and Exchange Commission (SEC) posed new rules covering the definition of exchanges that are required to and ongoing regulation by the Commission. Cryptocurrencies that are register with the SEC and comply on an ongoing basis with a complex set not “securities” generally fall under the regulatory ambit of the Com- of regulations (the “Reopening Release”) [63]. The Reopening Release modities Futures Trading Commission (CFTC) as “commodities.”80 was motivated largely by the goal of clarifying the SEC’s position on One branch of the Howey test requires investor dependence on the the applicability of the rules to token-based decentralized exchanges, “efforts of others” to make a profit as a necessary condition for a to- including those governed by DAOs [63, pp. 6–7]. As part of the new ken to be a security.81If the token is decentralized, in the extreme case rules, the SEC had proposed expanding the definition of an exchange where just the code runs on its own, arguably, there is no such depen- by adding a “group of persons that constitutes, maintains, or provides dence. Furthermore, disclosure of the backgrounds and plans of the key a market place or facilities for bringing together buyers and sellers of managing parties is a major objective of registration and ongoing reg- securities” to entities that can comprise an exchange [63, p. 6 (empha- ulation under the securities laws [59]. If there are no such parties, the sis added)]. Commentators pointed out that for decentralized projects, regulation loses its primary rationale. In addition, if there are no man- code replaces intermediaries, and a “group of persons” could include a aging parties, it is unclear who would be available to comply with the very wide range, including developers and miners. The SEC responded regulation in any event. first with the general principle that “[t]he existence of smart contracts An example in which the degree of decentralization affects the type on a blockchain does not materialize in the absence of human activity of regulation rather than creating a potential exemption from regulation 82 H.R. 4763 is known as the Financial Innovation and Technology for the 21st 78 The set of current regimes, even limited to the most important ones, is likely Century Act (“FIT21”). H.R. 4763 was approved by the House Financial Services to be obsolete within months, if not weeks, of publishing this paper. Committee on July 26, 2023 and passed by a strong bipartisan majority of the 79 SEC v. W.J. Howey Co., 328 U.S. 293 (1946). full House on May 22, 2024, creating the possibility of enactment if approved 80 A cryptocurrency can be both a “security” and a “commodity” under the ap- by the Senate and signed by the President [60,61]. plicable statutes and regulations, creating joint regulatory oversight by the SEC 83 The proposal defines both a “decentralized network” and a “decentralized and CFTC. Virtually all cryptocurrencies are considered to be “commodities,” governance system.” In each case, the focus is on whether there is a person and the CFTC has regulatory authority to police fraud and market manipulation with effective control. In the case of a “decentralized network,” there is also the in spot markets for commodities. The SEC has the same authority with respect requirement that no party has 20% or more of ownership or voting power. to cryptocurrencies that also are “securities.” 84 Commodity Futures Trading Commission v. Ooki Dao (N.D. Cal., Dec. 20, 81 SEC v. W.J. Howey Co., 328 U.S. 293, 299 (1946). 2022). 22 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 or a machine (or code) controlled or deployed by humans” [63, p. 22]. business” [64]. In a later videotaped interview, Commissioner Peirce The SEC then made clear the astonishing breadth of parties that might took the position that the Commission should “set true decentralized be included in the “group of persons” collectively held responsible for protocols aside” because the “technology itself is a substitute for many securities law compliance: interface providers, code developers, DAOs, of the regulatory protections” otherwise required when interactions are validators, and issuers and holders of governance tokens if they act in with “an intermediary, a centralized firm” [65].87 She noted that you concert or share common control [63, p. 27]. Related more directly to can lose money and get hurt but “you are opting into that when you are DAOs, the SEC stated that “... significant holders of governance or other entering into decentralized transactions” [65]. This approach is very tokens ... could also be considered part of the group of persons and similar in flavor to the newly enacted EU rule that exempts a crypto thus an exchange if they can control certain aspects of it” [63, p. 25]. application that operates “in a fully decentralized manner without any The aspects included: securities available for trading, requirements and intermediary.” conditions for participation, determining who can share profits or rev- The third regulatory approach, which can be termed regulatory grad- enues, or having the ability to enter into legal and financial agreements ualism, consists of observing a new technology and its operation and on behalf of or in the name of the market place or facilities [63, p. 25]. then, after a period of observation, deciding on a new, appropriate The SEC was not willing to exclude software developers, who, acting in- regulatory regime. Part of Commissioner Peirce’s dissent to the Reopen- dependently and separately from the project, published code that was ing Release advocated this approach. She pointed out with approbation later picked up and used in the project by an unrelated person. These that the SEC had used a regulatory gradualism approach in the 1990s, parties were only “less likely” to be acting in concert [63, p. 28]. The permitting new, electronic exchanges to operate for a period of a few SEC also made clear that liability exists for persons or entities that ini- years despite being noncompliant with the prevailing strict regulatory tially created or deployed the system’s code even though “the system, requirements for exchanges, resulting in the successful development and once deployed, typically cannot be significantly altered or controlled by implementation of a new body of regulations tailored to such exchanges. any such persons” [63, p. 29]. Closely related to this 1990s example is the idea of creating a “regula- The SEC went on to discuss compliance costs. The SEC noted that tory sandbox” in which new cryptocurrency technologies operate and “factors associated with certain technologies ... might increase compli- within which participants understand that they are on their own with ance costs” and that compliance might “significantly reduce the extent respect to possible losses prior to the imposition of an existing regula- to which the system is ‘decentralized’ or otherwise operates in a manner tory regime or the implementation of a new one.88If the dissenters gain consistent with the principles that the crypto asset industry commonly a majority on the Commission in the future, policy may well move to- refers to as ‘DeFi’” [63, p. 122]. The SEC singled out DAOs as a case ward this third approach or back to the first decentralization-focused for which the highest possible compliance costs might occur.85The SEC approach that would follow from classical adherence to Howey.89 continued, stating that “the holders of governance tokens, or other to- kens that carry voting rights, may bear the responsibility of ensuring 5.6.2. Interaction of the mechanism with regulation compliance with the system,” suggesting that the token holders should A key issue for both DAOs in general and for the mechanism in par- create an organization or delegate persons to undertake the activities ticular is the extent to which the associated technologies reduce the required for compliance, putting money into the DAO if the costs are need for regulation. “Regulatory equivalence” exists if elements in the not covered by fees [63, pp. 124–125]. Furthermore, the token holders technology achieve the same purpose as regulation.90 For example, to would have to have the power to alter the relevant smart contracts by the extent that DAOs and blockchain-based applications replace inter- voting if necessary for compliance, and in the case of immutable smart mediaries with code, they eliminate the need for regulation to address contracts, miners or validators would have to alter the smart contracts potential misbehavior by such intermediaries. via a hard fork [63, pp. 126–127]. Blockchain elements that typically accompany DAOs make not only While it is true that these positions were asserted in a Release solic- the governing code public and transparent, but also much, if not all, iting additional comments, they were the responses to concerns raised of the operations conducted by the DAO. This transparency reduces by previous comments suggesting that the scope of the Rules should be the need for many of the disclosures that regulators typically require limited to create an exemption or at least breathing space for decen- in order to protect investors by giving them information about their tralized projects, including DAOs. And although the Rules only apply to investments. Requiring such disclosures is a major focus of regulation exchanges, the same reasoning would apply to the inclusion of DAOs in in the United States and many other jurisdictions.91 In addition to re- the general category of “securities” subject to regulation.86 quiring disclosure, regulatory systems typically include market structure It also is noteworthy that the SEC was deeply divided concerning and procedural protections for investors, often aimed at promoting fair- the position taken in the Reopening Release, with the minority group in ness for such investors as they interact with sophisticated parties or the 3–2 Commission split being sharply critical of that position. Commis- sioner Hester Peirce articulated the critique in a dissent to the Reopening Release [64]. She characterized the Release position as an “approach to 87 Choi et al. [66, pp. 2–3, 7–9]described this situation as one that involves exchange regulation as something that must not—indeed cannot—be “functional and regulatory equivalence.” The application is the same as one altered to allow room for new technologies or for new ways of doing that normally would be regulated, functional equivalence, and elements in the technology achieve the same purpose as regulation, regulatory equivalence. 88 Commissioner Peirce has advocated this idea separately from her dissent 85 The Commission put it this way [63, pp. 124–125]: from the Reopening Release. See Piro [67]. 89 The SEC has five Commissioners appointed by the President, but only three The Commission preliminarily believes that a reasonable case, in which the can be from the same party. At the time of the Reopening Release, the 3–2 split highest possible compliance costs would result, would be a ... system that was along party lines, with the Republican Commissioners in the minority. Thus, performs exchange activities in part using smart contracts, but in which the regulatory approach can change sharply every time there is a Presidential control over changes to the smart contracts is given to a token-based vot- election. ing mechanism, which may use governance tokens as discussed above, and 90 See supra Footnote 87. where the tokens are dispersed among a large number of investors. 91 The preamble of the Securities Act of 1933, one of the two key statutes that form a basis for securities regulation in the United States, describes the 86 This reasoning would greatly weaken the scope of the “efforts of others” goals of the statute as follows: “AN ACT To provide full and fair disclosure of branch of Howey as a restrictive necessary condition for a token to be considered the character of securities sold in interstate and foreign commerce and through a security, and, if pursued, most likely would trigger legal challenges and a the mails, and to prevent frauds in the sale thereof, and for other purposes.” possible reconsideration or clarification of Howey itself. Securities Act of 1933, 15 U.S.C. §§ 77a–77aa (2018). 23

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 exchanges.92 An example is the rules governing tender offers in the that will maximize social surplus and attempts to distribute that sur- United States, offers that a bidder makes to shareholders of public com- plus in a manner that allows projects to reflect their true social value panies to buy their shares for a particular price at a specified time. These for the purposes of initial and ongoing investment. Excessive regula- rules require bidders to leave any offering open for at least 20 days, to tion would imperil these benefits. Finally, disclosure of the identity of refrain from giving different subscribers different terms, and to make the guiding parties of an enterprise is a major goal of securities regu- certain disclosures.93 Furthermore, management of the target corpora- lation. The diffusion of control in DAOs tends to make identification of tion is required to issue its opinion of the offering terms.94 managing parties and elucidation of information about them difficult The mechanism goes considerably beyond these customary disclosure- if not impossible. In contrast, by the operation of the mechanism, the based, market structure, and procedural protections to provide direct identity of the managing parties will be evident, at least during control substantive protection to investors. Consider, first, control period situ- periods. ations. Holding tokens at the beginning of an auction protects holders Do all of these features add up to a case for exemption? The answer to against any losses during the control period and guarantees that they that question is not clear. There may remain some scope for regulation. will realize the increase in value or its financial equivalent promised In particular, disclosure of certain information beyond that available by the control party on the portion of the tokens that they retain at from the transparency inherent in blockchain aspects may have value to the end of the auction. This arrangement exists whether or not the auc- market participants and potential auction bidders. We leave exploration tion results in a shift in control, as opposed to situations in which the of that possibility and the question of exemption to future work. winning bidder previously had control via an earlier auction or from a Aside from creating a general case for reduced regulation or a reg- token position combined with active participation in governance dur- ulatory gradualism approach, use of the mechanism raises four addi- ing an open period. More generally, the auction aims to transfer as tional considerations with respect to existing regulation under the three much of the social surplus from the control party’s operations as pos- approaches. First, there are the potential regulatory impacts from intro- sible to these token holders. This high degree of substantive protection ducing the mechanism into DAO governance systems. Second, the mech- in the face of shifts in control does not exist under current regulatory anism creates regulatory opportunities, ways in which DAOs could more regimes. easily fit within existing regulatory regimes without adverse impacts on The control period protections are not operative for token holders their mission and structure. Third, regulation may directly impact the during open periods and do not apply to tokens purchased during a effectiveness of the mechanism. Fourth, the mechanism raises regula- control period after the auction has been completed.95However, token tory questions if the DAO is subject to the core aspects of securities or holders in both situations enjoy two other protections. First, the threat commodities regulation. of future auctions has a disciplinary effect with respect to misbehavior The regulatory impact of shifting to the mechanism from the previ- or poor performance on the part of existing governing parties, including ous DAO governance regime is unclear. For decentralization-focused ap- the case in which a mass of diffuse token holders determine the DAO’s proaches, the impact of the mechanism on decentralization looms large, path.96Second, these groups will enjoy future control period protections especially in Europe, where a finding that the DAO provides “services ... if subsequent auctions arise. in a fully decentralized manner without any intermediary” would lead to The substantive investor protections inherent in the mechanism both substantially strengthen the case for applying a less burdensome regu- exemption. As mentioned above, the possibility of asserting temporary latory regime to DAOs that employ it and create the prospect of more contestable control created by the mechanism arguably enhances de- fully protecting investors than existing regulatory regimes do. They also centralization compared to current DAO governance. At the same time, make a DAO using the mechanism a very attractive candidate for inclu- visible control during control periods creates the opposite impression. sion in a regulatory sandbox or for temporary forbearance by regulators The outcome is uncertain, especially given that the EU rules are brand under regulatory gradualism approaches. new. There are additional ways in which the mechanism advances the case In the United States, the creation of control parties by the mechanism for a milder form of regulation as well as for regulatory gradualism. As can lead to the claim that the “efforts of others” branch of the Howey we have seen, there is a strong argument that the mechanism enhances test is met because, in the words of Howey, the control party’s efforts decentralization in the face of both implicit and explicit control possibil- are the “undeniably significant ones,” essential to overall success and ities, and in many cases actualities, that emerge from token ownership profitability. Contestability likely is of no help here, given the disclosure and voting regimes. The mechanism induces choice of the path forward rationale of the securities laws. Even if control is for a brief period, investors would profit from knowing about the background and plans of the control party in deciding whether to invest or divest. On the other 92 A good statement of these purposes is the preamble of the Securities Ex- hand, it is clear that large token holders and parties that participate in change Act of 1934, the second in time of the two key acts aimed at protecting implicit control would be in the same boat under Howey. investors in the United States: “AN ACT To provide for the regulation of secu- The mechanism creates some regulatory opportunities, ways in rities exchanges and of over-the-counter markets operating in interstate and which a DAO may fit more easily within regulatory regimes without foreign commerce and through the mails, to prevent inequitable and unfair compromising its central purposes. At least during control periods, there p E r x a c c h t a ic n e g s e o A n c t s u o c f h 1 9 e 3 x 4 ch ( a J n u g n e e s 6 a , n 1 d 9 3 m 4 a , r c k h e . t s 4 , 0 a 4 n , d ti t f l o e r I o , t § h 1 er , 4 p 8 u r S p ta o t s . e 8 s. 8 ” 1 S ) e . curities is a clear party who can coordinate and interact with regulators, paral- 93 15 U.S.C. § 78m; 17 CFR §240.13e, §240.14d, and §240.14e. lel to the managers of a traditional corporation. This is not the case if 94 Rule 14d-9 [17 CFR §240.14d-9] and Schedule 14D-9 [17 CFR §240.14d- there is only implicit control or a group of large token block holders. The 101]. ability of the control party to interact with regulators creates a shield 95 The protection against losses and the guarantee of claimed gains applies to for other parties, such as developers, validators, and token holders. This the particular holders at the time an auction is completed rather than attaching shield may be especially valuable in the face of a joint and several re- to the tokens themselves. Thus, buyers during a control period do not enjoy these sponsibility regulatory approach, such as the one suggested by the SEC protections. See supra Page 17, near the end of Section 4.3.1. Passive, “buy and in the Reopening Release, which envisions a very broad set of actors hold” investors enjoy particularly strong benefits overall because they always being subject to potential regulatory obligations and liabilities. Other- b 9 e 6 ne B fi e t c a fr u o s m e a t u h c e t i c o o n n s t r m ol a p y e b ri e o d fr e p e r l o y t e in ct i i t o ia n t s e . d at any time and because the auc- wise, this approach might well, in the words of dissenting Commissioner tions are not subject to the restrictions that typically apply in corporate regu- Peirce, “render innovation kaput” [64]. latory regimes, the threat implicit from auctions under the mechanism is most Some aspects of regulation may make it easier to implement the likely a much more effective external governance device than the threat from mechanism itself. As discussed above, one of the biggest challenges for conventional corporate takeovers. the mechanism is toehold reporting. If the DAO is a security, thenSched- 24 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 ule 13D reporting or a modified version of it would apply, creating a 5.7. Implementation uncertainties and challenges legal obligation to report a non-negligible toehold position.97This legal obligation and its enforcement are external, not a code feasible part of We have discussed various implementation uncertainties and chal- the mechanism itself. Nonetheless, it could go a long way toward filling lenges in the previous parts of the paper. This subsection provides an what might be a significant implementation gap for the mechanism. integrated view and summary, one that extends the previous discussion Even if the DAO is not considered a security under U.S. law, it will be on several fronts concerning the elements that give rise to the uncer- considered a commodity if it is publicly traded and thus subject to the tainties and challenges, and how those elements interact. ability of the CFTC to police fraud. The DAO can leverage this potential In Section 4.1.4, we described potential difficulties with respect fraud liability with respect to the toehold position. Being able to submit to toehold reporting, perhaps the major operational challenge for the an artificially low bid by failing to report the entire toehold position is mechanism. As discussed in that subsection, toehold reporting is vital fraud. The full enforcement and adjudication power of the CFTC comes for the integrity of the bidding process and for enforcing the market into play. The control party would be subject to discovery and required liquidity constraint. If a bidder fails to disclose that bidder’s toehold testimony under oath. Hiding part of the toehold would create poten- position, part of the amount of the increase in token value claimed un- tially serious consequences for the control party. This potential fraud der the bid as flowing to the other token holders actually will go right liability is another external device, not part of the code feasible core of back to the bidder to the extent of the concealed toehold position. The the DAO, but again, it can help address a difficult implementation gap claimed amount is inflated. Since that claimed amount is the touchstone of the auction that determines the winner, a bidder whose business plan for the DAO.98 is in fact inferior to the business plans of one or more other bidders can The mechanism rules may have legal and regulatory implications prevail. Similarly, if part of the market liquidity cushion actually con- if the DAO is held to be a security or if it is an exchange subject to sists of a concealed toehold position, the actual cushion will be smaller SEC or CFTC registration and oversight. If the DAO is a security, then than that mandated by the constraint. In that case, there will be less in the United States, various state and federal laws covering corporate market depth, and market manipulation by the control party will be governance might apply. Although the mechanism does not involve a easier. tender offer or a merger, it is possible that state corporate law requiring We noted some possible measures to enforce toehold reporting, in- shareholder (here token holder) votes for certain actions might apply cluding the use of bounty hunters and the implementation of a suitable to the auctions. The freeze-out feature might be the subject of scrutiny registration system requiring know-your-customer verification. In our even though it treats all of the 𝑇 1 token holders the same. Jurisdictional view, the most promising approach is to build a flush sale into the mech- issues are present. State law generally will not apply unless the DAO is anism. The flush sale involves the purchase of all of the tokens other incorporated in the state. The ways in which this class of rules applies than the control party’s deposit, rather than just purchasing the amount and the extent to which they apply at all are complex, and we leave required to complete the freeze-out step. A registration process is avail- full consideration to future work. The inquiry is important because it able for parties to certify that they are not the control party or related also addresses the question of whether the mechanism here could be to the control party. Then, the non-freeze-out portion is auctioned off to used more generally rather than being limited to DAOs. In particular, registered parties in order to restart the token market, with the surplus the strong points of the mechanism are equally cogent for traditional from the auction compared to the flush sale price, if any, distributed to corporate governance. registered parties who held tokens prior to the flush sale. The effective- Finally, there are legal considerations in addition to regulation. Most ness of the registration system and the question of whether a sufficient prominent is the issue of legal liability for DAO participants. This issue number of parties would register is a significant uncertainty. In addition, exists with or without the mechanism. DAOs can be “wrapped” in LLC or there are token market liquidity issues, which we discuss below, along other legal forms to provide limited liability for participants, including with other such issues. More generally, there is the uncertainty about token holders and any parties that might be seen as “management.”99 whether any of the potential solutions to the toehold reporting problem Limited liability might be particularly valuable for the control party due will suffice alone or in combination. As we have noted, the stakes for to the high visibility of being in that position. This is the main new ele- the mechanism are significant. ment created by the mechanism. The question of the legal status and use At several points, we have mentioned the importance of capital mar- of wrappers is a quickly developing field, and the choices are complex. ket adequacy for the functioning of the mechanism. The required de- We do not discuss that question further here. posits in order to bid are very large, of the same order of magnitude as the pre-auction value of the DAO. There need to be parties capable of shouldering this burden or providing capital to support bids by parties who do not have sufficient resources on their own. 97 Under Section 13(d) of the Securities Act of 1934, any person who “directly Capital market adequacy has a critical influence on bid intensity, the or indirectly” becomes the beneficial owner of more than 5% of any class of number of actual or potential bidders present in a particular auction. Bid registered equity securities, and certain equity securities that are exempt from registration must, within ten days, report certain information to the issuer, to intensity, in turn, affects the ability to shift as much of the social surplus any exchange on which the security is traded, and to the SEC. “[I]f the purpose arising from the control party’s business plan as possible to the other to- of the purchases or prospective purchases is to acquire control of the business ken holders, a major goal. As discussed in Section 4.1.2and illustrated of the issuer of the securities,” the information must include “any plans or pro- in Fig. 2, the winning bidder can appropriate surplus up to 𝐴∗ 1 −𝐴∗ 2 , posals which such persons may have to liquidate such issuer, to sell its assets to the difference between the winner’s best possible bid and the runner- or merge it with any other persons, or to make any other major change in its up’s best possible bid. These numbers represent the amount of social business or corporate structure.” Securities Exchange Act of 1934, Pub. L. No. surplus promised to the other token holders, a promise that is a com- 73–291, 48 Stat. 881 (codified at 15 U.S.C. §78a (2012)). Schedule 13D is the mitment in the face of the deposits. Higher bidding intensity will tend to form used to make the disclosures required by Section 13(d). increase 𝐴∗, which represents the actual amount of social surplus trans- 98 It also might be possible to create some structure in the DAO to aid the ferred to th 2 e other token holders, reflecting greater success in practice a a p u p ct l i i o ca n b a il n it d y t o h f e th to is e h li o a l b d i l r i e ty p . o F rt o in r g in o s b ta li n g c a e t , i o th n e t o D A th O e m CF ig T h C t , t o ri r g , g i e f r t h n e o t D ic A e O o f i s a n a for the mechanism. In addition, as discussed in Section 4.1.3, bidding security, to the SEC, along with disclosure of the identity of the control party. intensity is an important parameter with respect to collusion. Collusion The CFTC and the SEC could incorporate this notice into their regulatory regimes in an English auction can encompass parties who would have been the as a trigger for possible inquiry. runner-up, causing the winning bidder and the colluding group to cap- 99 See, e.g., Guillaume and Riva [41], Guilluame and Riva [68], Kerr and Jen- ture more of the social surplus versus the other token holders. If there nings [69], Jennings and Kerr [70], and Brummer and Seira [71]. are a large number of bidders, and especially if a significant number 25 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 have best bids close to 𝐴∗, then collusion will be more costly to orga- in response if the mechanism is employed. We have seen multiple in- 1 nize and may be much less effective. In the extreme case of “infinite” stances in which the investment or trading aspects of capital market bidding intensity, there is a continuum of bidders with 𝐴∗ 𝑖 values run- adequacy come into play. It is hard to assess either of these aspects out- ning up all the way to 𝐴∗. In that case, the other token holders receive side of an actual implementation. We have noted that with respect to the 1 all of the social surplus for certain, and collusion is not a threat. investment aspect, there may be a substantial set of institutions that can Capital market adequacy is not limited to the presence of enough act as bidders or bid financiers for auctions involving even the largest high-quality investors who can serve as auction bidders or who can sup- DAOs at present. However, this static observation is a limited part of the port others who bid. Aside from this investment aspect, capital market picture. If the auction mechanism is implemented, given the potential adequacy also has a trading aspect, the ability of traders, large as well as profits from winning the auction or from financing parties who do so, it small, to provide enough liquidity to support the successful operation is likely that a new group of institutions and potential bidders attentive of the mechanism. The two aspects are related at the practical level be- to possible and actual auctions will arise in response. To what degree cause parties who are potential bidders or who are able to financially these tendencies will create bid intensity is not clear. Capital market back bidders with the required deposits may also be major informed adequacy may also vary depending on the characteristics of particular traders in the relevant market. For instance, in mature equity markets, DAOs in ways that are not entirely predictable. For example, smaller there are institutions that are both major portfolio investors and also DAOs require less capital, but the potential rewards are also smaller. governance activists that selectively intervene, including by encourag- The same uncertainties apply to the trading aspect. A group of traders ing or initiating takeovers or mergers.100 may arise that is particularly attuned to DAO auctions, including poten- As we discussed in Section 4.3.1, the quality of trading markets af- tial aspects such as token auctions following flush sales. Auctions are fects the feasibility of market manipulation with respect to prices at salient events and may give rise to increased liquidity when they occur. discrete points in time that the mechanism employs to settle value and This phenomenon may mitigate the risks of market manipulation by bid- surety deposits or to set auction parameters. Parties may attempt to ma- ders or control parties. However, again, it is hard to predict what the nipulate market prices at such times, perhaps combined with choosing actual trading response will be and how it might vary across different the timing of actions such as initiating an auction or abandoning control. DAOs. In Sections 4.1.4and 4.3.1, we considered the possibility that control Layered on top of these capital market considerations are uncertain- parties would manipulate prices upward through purchases to reduce ties about regulatory responses and the fact that DAOs can take measures losses associated with their value or surety deposits, followed by dis- themselves if capital markets have limited effectiveness. For example, posing of the purchased tokens at the subsequent high price levels, a if regulators are very active in policing market manipulation, the pres- “pump and dump.” Policing of market manipulation by regulators is ence of potential market responses that can defeat such manipulation is one counter, and the mechanism can include countermeasures such as less important. And if market and regulatory policing of market manip- computing reference prices equal to the average market price during a ulation of spot prices prove to be inadequate, DAOs can take steps such time interval surrounding the crucial date, with some loss of accuracy. as using reference prices averaged over a time window rather than spot However, as we have noted, if trading markets are developed enough prices at one point in time to determine outcomes such as the refund- and active, short sellers might defeat the attempt to manipulate prices ability of deposits. upward.101 Resolving either the market uncertainties or uncertainties about the Other considerations that make the trading aspect salient involve the effectiveness of various methods to assure accurate toehold reporting operation of the mechanism itself. For example, if a flush sale approach requires trying out the auction mechanism in real-world settings.102And is used to address the toehold reporting problem, all of the tokens are the details of the settings, including the characteristics of the particular purchased at the pre-auction price. The market is then restarted by auc- DAOs involved and the markets in which they are embedded, are likely tioning off some of these tokens to a restricted class of purchasers. There to have a large impact on the outcomes. clearly is a question of whether enough diverse purchasers will step up to purchase enough tokens to reestablish an active and robust token 6. Concluding thoughts market. Closely related to the trading aspect is the market reception for DAOs We have shown that there is a plausible mechanism for DAO gov- that include the mechanism, both when the mechanism is added and ernance that is code feasible, EV-robust, and efficient in the sense that as it operates over time. Clearly, there are many attractive aspects of it favors the business plan with the highest social surplus. The auction the mechanism. It tends to maximize the share of social surplus from aspect of the mechanism provides a way out of the potential indetermi- innovations that ordinary investors will receive. Investors at the initia- nacy and pathologies that arise from pure voting mechanisms. At the tion of the auction are placed in a riskless position with respect to the same time, the sequential aspects of the mechanism create the ability to gains claimed to be possible by the winning bidder. At the same time, secure and enhance value that stems from DAO voting and other non- the freeze-out feature forces investors to sell a portion of their hold- market governance approaches. The fact that empty voting is irrelevant ings at the pre-auction price. Although this feature plays a key role in to prevailing under the mechanism also removes the possible arbitrari- allowing ordinary investors to capture innovation gains with low risk, ness or deliberate harm that might result. The mechanism permits the the operation of the feature may be disconcerting. However, as men- possible resolution of some major regulatory dilemmas and creates a tioned in Section 3, mergers create a similar freeze-out effect and are a strong case for a reduced level of regulation that is nonetheless at least routine and unobjectionable aspect of many public equity markets. Fi- equally effective. The mechanism tends to minimize the added token nally, it is likely that some investors will be more attracted to the DAO value received by project creators, thereby tending to maximize the in- because of the presence of the mechanism, and others will be less at- vestment value of the project, albeit imperfectly. tracted. The classic finance phenomenon of clientele effects comes into All of these qualities are very positive. In the previous subsec- play: The clientele for the DAO will shift to include investors for whom tion, we addressed implementation uncertainties and challenges, which the mechanism is an attractive feature. We have summarized a large set of implementation challenges. It is difficult to predict the severity of the challenges and what will emerge 102 Simulations and experiments are not likely to be helpful. The effect of factors such as the availability of parties to enhance bid intensity or of traders to provide liquidity is straightforward. Simulation and experiment outcomes will reflect the 100 See Footnote 42supra. underlying assumptions about these factors in an obvious way. Observation in 101 See Footnote 55supra. real-world settings is required to make meaningful headway. 26

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 raises the question of whether the mechanism can match its theoretical These approaches and the ensuing wisdom of crowds or attractive ag- promise in practice. In the rest of this section, we turn to a different but gregative properties would operate fully during the open periods in- quite significant inquiry: How does the mechanism appear when con- terspersed among control periods. Furthermore, even during control sidered in light of Web3 and DAO governance norms? periods, the control party can abstain partially or fully on particular One idealism of some Web3 enthusiasts is that DAOs will create a votes in order to allow the aggregate benefits of voting to be realized new kind of democratic community that is free from exclusive focus based on the control party’s calculus of how much expertise it has on on token value or domination by monied parties. It is not clear if the those votes compared to the mass of other voters.104Some DAO projects token value critique is apt for economic DAOs, which are character- already conform to a rigid version of this more flexible possible control ized by token value being a measure of the value of the DAO activities. period behavior. A foundation or other centralized element implicitly or As discussed in Section 1, cases of economic DAOs extend way beyond explicitly makes certain decisions with respect to the DAO, while others DAOs that primarily have a commercial purpose. Rather than being an are left entirely up to the decentralized DAO governance mechanism. evil, token value in the case of economic DAOs creates the opportunity The auction mechanism here could extend to some current projects as to provide superior governance through mechanisms, such as the one a unified whole, encompassing both the centralized and decentralized detailed here. portions of the projects. This approach would create on-going flexibility With respect to community, “democratic” has many possible mean- to allocate decisions between voting mechanisms and more centralized ings. Here, we have taken the position that the goal is to maximize the methods in the overall enterprise by using control periods to restruc- value of each DAO project with respect to an extended community that ture the balance between the on-going centralized and decentralized includes both present and potential future participants. That value in- elements. This ability to renew and redesign the structure in a coherent cludes process value inhering from “democratic” aspects of DAO voting way would be perpetually available. or other nonmarket DAO governance mechanisms. If present or poten- This perpetual ability to renew and redesign the unified enterprise tial token holders value certain democratic elements in excess of any also addresses another rigidity, one that is intertemporal. Many enter- associated losses from weaker operational performance, the mechanism prises begin with centralized incubation of the DAO element and then will favor those elements. reach a point where governance passes entirely to a “fully decentralized” More generally, the mechanism permits an infusion of new partici- state, relying only on the DAO governance mechanism.105One potential pants and approaches with respect to both DAO operation and gover- serious problem with this approach is that the enterprise may benefit at nance. It is impossible for large token holders, including founders or a later point from a major reorganization or revamp, perhaps with inno- parties holding a token majority, to retain control if there are parties vation in mind, that is critical to maintaining ongoing dynamism or even who will outbid them in an auction. This openness to innovators seems for the survival of the project.106This reorganization or revamp may be solidly in the spirit of DAOs, especially given that the auction mecha- difficult or impossible to accomplish without reinstating a later period nism places them on an even footing with the current governing interests of centralization that incubates a rebirth of the DAO in a renewed and in the DAO, who also can bid and win. more valuable form.107It is very hard to see why restricting centraliza- Observers have pointed out that many DAOs currently are “undemo- cratic” due to implicit control by founders or others who may have relatively large token holdings while being surrounded by many small, mechanism, there is no continuing private property right in controlling the DAO. disinterested holders of the rest of the tokens. It may be that this situa- Instead, it is sequentially “rented out” to winning auction bidders, those who of- tion is a tendency inherent to governance through token voting, with f s e o r c i t a o l p s a u y r p t l h u e s h t i h g e h y e s c t a a n m g o e u n n e t r a o t f e “ d re u n ri t n ” g i n a t h te e m fo p r o m ra o ry f p “ a te r n t a o n r, c y id ” e p al e l r y i , o a d l . l L o a f l t l h ey e implicit control shifting from one group of such parties to another. and Weyl [72]associated this kind of approach with Henry George and William In that case, DAOs are already characterized by a succession of con- Vickery. trol parties, and the auction mechanism only creates a more efficient 104 See Bar-Isaac and Shapiro [73]. and fair way to implement that succession. Fairness here is not only 105 MakerDAO is a prominent example. Maker Foundation was a centralized with respect to potential control parties who are freed from elements entity used to develop the MakerDAO system. As described in MakerDAO [74], such as empty voting, but also with respect to smaller, more passive the Maker Protocol Whitepaper: holders. These holders may be portfolio investors or may be less ac- tive for Jensen-Meckling reasons: The benefits of the costly effort to The Maker Foundation currently plays a role, along with independent actors, become informed will accrue almost entirely to others. The mecha- in maintaining the Maker Protocol and expanding its usage worldwide, while nism encourages value-increasing transitions and attempts to distribute facilitating Governance. However, the Maker Foundation plans to dissolve once MakerDAO can manage Governance completely on its own. a significant proportion of the resulting social surplus to the passive holders. In July 2021, MakerDAO reached a point described by the Maker Foundation It is important to note that the auction mechanism does not ban con- CEO as being “completely decentralized,” with the transfer of all Foundation ventional voting or vote-buying regimes such as quadratic voting.103 functions to the DAO and the subsequent envisioned formal liquidation of the Foundation [75]. 106 Exactly this situation appears to have emerged for MakerDAO. Only a short 103 As discussed in Lalley and Weyl [72], when quadratic voting operates well, time after it presumably became completely decentralized, see Footnote 105 it aggregates preferences and information accurately with respect to decisions. supra, Rune Christensen, one of the co-founders, used his large token posi- It is doubtful that quadratic voting could play a strong role in the context here tion to initiate a major reorganization of MakerDAO through a project called in the face of asymmetric information and the possibility of free-riding. Parties “Endgame.” The goal was to bring MakerDAO to the point where it could op- without adequate information about potential control parties will not be able erate at a mass market level. Because of Christensen’s dominant token position, to represent their own interests well by voting, and the revelation of informa- implementation of Endgame came about through an effective re-centralization tion will trigger free-riding. If a project creator expends a large amount in a of the project, a step that Christensen envisioned as temporary. See Gilbert [76]. quadratic vote, the project creator will not be able to cover it from the added 107 Relevant in this regard is Vitalik Buterin’s lament concerning Ethereum in token value due to that free-riding. If the DAO returns amounts that the creator 2022 [77]. Buterin stated that he had “diminishing influence” over Ethereum paid for the votes required to prevail to the creator, voting incentives are dis- and that it was “becoming harder to make big changes to the Ethereum pro- torted. tocol due to the many stakeholders that have a say in the decision-making The mechanism described here fits solidly within a category that Lalley and process,” creating an Ethereum that was “definitely more vetocratic.” He stated Weyl [72, p. 36] described as “the natural private goods markets analog of that: “Even now, I feel like the window is closing on substantial things. It’s get- the radical market logic of [quadratic voting],” namely “assets ... being con- ting harder to do big things even today.” Ethereum is not governed by a DAO, tinuously auctioned for rental according to ... [an] English auction.” Under the but the possibility of getting to a stale point is equally applicable to DAOs. Re- 27 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 tion to the beginning of the project is optimal in general. The auction compute the strongest potential bid, (𝑆,𝑅,𝑡 𝑏), the one that maximizes mechanism leaves open the possibility of major reform during a con- 𝐴=(1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞−𝑅, based on the plan. trol period by enabling consistent and coherent execution of a new plan The total social surplus generated by the plan is 𝜓=(𝑉 −𝑃 )𝑞−𝐶. 0 similar to the plans used to birth DAOs during an initial period of cen- Consider first the case 𝑆≤𝑉. In that case, the bidder’s profit function tralized incubation. A control period for major reform can be invoked conditional on winning the auction based on a bid (𝑆,𝑅,𝑡 𝑏)is: through the mechanism on a when-needed basis, with the most promis- 𝑅 ing plan the odds-on favorite to be implemented. Π𝑏=𝑡 𝑏(𝑉 −𝑃 0 )𝑞−𝐶+ 𝑆−𝑃 (𝑉 −𝑃 0 ). We believe that the mechanism described here fits well within the 0 ideals that have inspired DAOs. Control over the direction of the DAO The first term, Π𝑡𝑏 =𝑡 𝑏(𝑉 −𝑃 0 )𝑞, is the bidder’s expected profit on the u p T a n h r d e t e i D e r s A t h O c e a i n s m s n e a o c f h e l a o f n o n i r g s e m d r e m i m s o a c c i o n r n a ta t c i i y n n u o a o f n u v s a i l r r y i o o c n u o s g n r k t i e i p n s t d a t s h b r b l o e e . u c g F a h o u u s i e n m d a p e n l r i s a c u i a t c n t c d i o o n o n t t r f h o o e l l r - . b T 𝑡 𝑓 i h d 𝑞 e d ( 𝑉 e se r’ − c s o 𝑃 t n o 0 d e ) , h t e o is r l m d th t e i o s k b t e i h d n e d s , e b r w i ’ d s h d e i e c x r h p ’s e h c c a t o e v s d e t . p v T r a h o l fi e u e t t h o 𝑃 i n r 0 d th a t t e e r t p m h r e o , p t 𝑆 i o m − r 𝑅 t 𝑃 e i 0 o ( o n 𝑉 f 𝑡 t 𝑓 − he o 𝑃 f 0 b t ) i h d = e . lowed by a control period can correct the adverse consequences of voting total 𝑞 tokens for which the bidder has forced purchase or voluntarily mechanisms if necessary, defeat empty voting if it becomes a problem, sold at price 𝑃 0 using the freeze-out feature of the auction mechan(ism. and overturn attempts of malicious actors to damage the DAO. The inter- To create the best possible bid, the bidder will choose 𝑅= 𝑆−𝑃 0 𝐶− e i i s s s t f m s a T c a o h i x f l e i i p m t g a a o i s t z e s a e i d l v d . h e t e s o r m e t a h h l e l a h s b o e b l n e d e e e fi n r t s t o o a f r p e a r p l e l r s p o e a t n e r t c t i o t c e n i d p e . a p T n o h ts s e . s i v C b a o l l e n u s e m t r o e u f c c t h t h a i e v n e D is i A m n O n t o h p v a r a o t t j h i e o a c n s t Π s Π iz 𝑡 𝑏 𝑏 e = ) c w 0 o . n h A s ic t s r h s a u i i n m s t t e h 𝑡 𝑓 f e o ≤ s r m t 𝑡 h 𝑚 a e l − l e m s 𝑡 t o 𝑏 m 𝑅 re e q s n u u t b i t r j h e e a d c t t f t t o h o r i t s a h v v e a a c l l u o id e n s o b t f i r d a 𝑅 . i n T s t a h o t e i f n s fi b : r e e s a t k h 𝑉 i e n − g 𝑃 m 0 e a v rk en et , promise. No claim is made that this mechanism is the best one. We have 𝐴=(1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞−𝑅 suggested alternatives for a variety of mechanism aspects throughout. 𝑆−𝑃 [ ] If this kind of auction-based approach is found to be promising, there is = 𝑉 −𝑃 0 (1−𝑡 𝑏)(𝑉 −𝑃 0 )𝑞−𝐶+Π𝑡𝑏 much more work to be done. 0 𝑆−𝑃 [ ] = 0 (𝑉 −𝑃 )𝑞−𝐶 . CRediT authorship contribution statement 𝑉 −𝑃 0 0 Clearly 𝐴is maximized by the choice 𝑆=𝑉, which yields: This article has only one author, who did all the work. [ ] 𝐴= (𝑉 −𝑃 )𝑞−𝐶 . (1) 0 Declaration of competing interest 𝐴is the total social surplus from the business plan, which equals the so- cial gain from implementing it. It represents the strongest bid conditiona l The author declares that he has no known competing financial inter- on adopting this business plan. ests or personal relationships that could have appeared to influence the But there may be a better business plan that produces even higher work reported in this paper. social surplus, and 𝐴∗, the best overall bid, will emerge from maximizing total social surplus, 𝜓(𝐶)=𝑉(𝐶)𝑞−𝐶. Assuming that 𝑉(𝐶) is twice Acknowledgement continuously differentiable, that 𝑉′(0)>0, and that 𝑉′′(𝐶)<0, there will be a maximum defined by 𝐶∗=argmax𝐶 𝑉(𝐶)𝑞−𝐶, and 𝑉∗= I am grateful for valuable comments from Bobby Bartlett, Dan Boneh, 𝑉(𝐶∗). The strongest possible bid from a bidder characterized by the Albert Choi, Mike Guttentag, Jake Hartnell, Henry Hu, Takuma Iwasaki, value function 𝑉(𝐶)is: Silke Noa Kumpf, Mark Lemley, Sven Riva, Roberta Romano, Martin [ ] Schmidt, Mike Simkovic, Connor Spelliscy, Jay Yu, and two anonymous 𝐴∗= (𝑉∗−𝑃 )𝑞−𝐶∗ . (2) 0 referees as well as from participants at the DAO @ LexTech Institute 2023 Conference, the 2024 Stanford Blockchain Governance Summit, So far we have ignored the possibility that a pair (𝑉,𝐶) and, in the Stanford Law School Faculty Workshop, the TLDR Conference 2024, particular, (𝑉∗,𝐶∗) is infeasible because it violates the market size the 2024 American Law and Economics Association Annual Meeting, constraint 𝑡 𝑓 ≤𝑡 𝑚−𝑡 𝑏 required for a valid bid. In the case of a break- Edge Esmeralda 2024, UBRI Connect 2024, and the Hackers Congress even bid, violating this constraint means that the bidder cannot acquire Paralelní Polis 2024. I have also benefited greatly from conversations enough tokens through the freeze-out feature combined with the bid- with Andy Hall. der’s toehold position, if any, to cover the cost 𝐶 through added token value realized on the bidder’s token position. The bidder can acquire at Appendix A most the proportion 𝑡 𝑚 of the total tokens by these means. Note that if 𝑡 𝑚=1, violation of the constraint implies that 𝜓(𝐶)<0. In that case, the business plan destroys value. A.1. Proofs For a pair (𝑉,𝐶), the highest possible break-even bid requires 𝑅= We construct a proof of Proposition 1 and Corollary 2, proving 𝐶 ch − oic ( e 𝑉 o − f 𝑅 𝑃 0 a ) l 𝑡 o 𝑏 n 𝑞 g , i w .e i . t , h p 𝑆 ro = po 𝑉 si , n w g h a i n c h 𝑅 is t n h e a c t e j s u s s a t r y c o fo v r e r t s h e th b e r e c a o k s - t e 𝐶 ve . n T b h i i d s Lemma 1 and Corollary 1 near the end of the main proof when the to be the highest, result in: Lemma is needed. invo S l u v p e p s o e s x e p t e h n a d t i n a g p e o ff te o n r t t i , a c l o b n id si d st e i r n g ca o n f i l m ab p o le r m an en d t r a e s b o u u s r i c n e e s s s e q p u la iv n a t l h en a t t 𝑡 𝑓 = (𝑉 − 𝑅 𝑃 0 )𝑞 t m o o 𝐶 ne m ta o r n y e u ta n r i y ts . u n D i e t fi s, n i e n 𝑉 ord = e 𝑉 r t ( o 𝐶 i ) n = cr 𝑁 ea ( s 𝐶 e ) t ∕ h 𝑞 e + va 𝑃 lue t o o f b t e h e th D e A t O ok b e y n 𝑁 va ( l 𝐶 ue ) = (𝑉 − 𝐶 𝑃 )𝑞 −𝑡 𝑏 . 0 0 emerging from this business plan. The basic auction is a vehicle for the The market size constraint becomes: potential bidder to gain control in order to implement the plan. We 𝐶 (𝑉(𝐶)−𝑃 )𝑞≥ . 0 𝑡 𝑚 o w r o g r a l n d i . z I a t t i i o s n n o an t d c le m a a r jo w r h r y e v D a A m O p s s o a r r e E t f h re e q re u u e m nt w in o u th ld e b co e r a p n o y ra d te iff a e n r d en n t o w n i - t p h r o r fi e t - If the constraint is binding, then 𝑉′(𝐶)= 𝑡𝑚 1 𝑞 versus 𝑉′(𝐶)= 1 𝑞 in the spect to the possible benefits of occasional major overhauls. case of unconstrained optimization. The higher value of 𝑉′(𝐶)implies 28 J.Strnad Blockchain: Research and Applications 6 (2025) 100306 lower values for 𝑉∗, 𝐶∗, and the social surplus, 𝜓∗, in the constrained 𝑉 is private information of the bidder, not known by the mechanism optimization. Equation (2) still applies, but with these lower values. designer. Including a value claim with 𝑆 >𝑉 will be a dominated Given a lower value for the social surplus 𝜓∗, the consequent bid, 𝐴∗, strategy for any value of 𝑉 ∈[𝑃 ,𝑆] if and only if 𝛿(𝑆,𝑉)>0 for 0 also will be lower. all values of 𝑉, establishing Lemma 1. Corollary 1 follows because Suppose that the bidder in fact can make the highest break-even bid 𝐷 𝑣 ≥𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑃 0 )=(1−𝑡 𝑑)(𝑆−𝑃 0 )𝑞+𝛿(𝑆,𝑃 0 )and 𝛿(𝑆,𝑃 0 )>0. 𝐴∗of any of the auction participants and that the second highest break- 1 even bid is 𝐴∗ 2 . Then the bidder can capture 𝜓 𝑒=min{(1−𝑡 𝑚)𝜓∗,𝐴∗ 1 − A.2. Hedging and stochastic adjustments 𝐴∗} of additional social surplus from the business plan (𝑉∗,𝐶∗). The 2 bidder accomplishes that by adding 𝜓 𝑒 to 𝑅in the bid as if it were an We developed the sequential auction mechanism in a deterministic additional cost, which will reduce the bid by 𝜓 𝑒.108Retaining the busi- setting where changes in the token price are driven solely by winning ness plan (𝑉∗,𝐶∗) and adjusting 𝐴∗ 1 as indicated dominates changing bidder business plan innovations. We now assess the mechanism in a the business plan and submitting a different bid based on the alterna- stochastic setting, first discussing winning bidder hedging strategies and tive plan. Because the alternative plan will result in total social surplus then possible mechanism adjustments that, in effect, provide hedging at 𝜓 𝑎 <𝜓∗, a bid based on the alternative plan that directs the same the DAO level. amount of social surplus to the bidder will be lower than the corre- Honest bidders, those that are not aiming to engage in strategies sponding bid under the original plan. such as value destruction, enter an auction because they believe they Now consider the case 𝑆>𝑉. We will contrast this case with the can enhance the value of the DAO and potentially profit from those en- previous one in which the optimal value claim was 𝑆̄ =𝑉 accompanied hancements themselves. Doing so in a stochastic environment involves by a surplus claim of 𝑅̄ and an auction parameter 𝐴̄ . The value claim taking a risky token position and exposing themselves to potentially los- 𝑆>𝑉 will cause the bidder to lose 𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑉)from the functioning ing part or all of their value deposit or surety deposit due to token price of the value deposit forfeit function because only the level 𝑉 <𝑆 is fluctuations not associated with the effectiveness of their efforts to add attainable through the bidder’s efforts. As a result, the bidder’s profit value. In addition, unless offsetting adjustments are made, these stochas- function will include an additional negative term compared to the 𝑆≤𝑉 tic elements will tend to create imbalances in winning bidders’ portfolios, case, becoming: especially if the required position in the DAO is large relative to the other 𝑅 positions in those portfolios. As a result, winning bidders will want to Π𝑏=(𝑉 −𝑃 0 )𝑡 𝑏 𝑞−𝐶+ 𝑆−𝑃 (𝑉 −𝑃 0 )−𝜙(𝐷 𝑣 ,𝑃 0 ,𝑆,𝑉). hedge the position they are taking in the DAO. We sketch how the hedg- 0 ing might operate, leaving aside a more formal development in favor of Furthermore, to maintain the same amount of added token value that creating an accurate but more intuitive perspective. would accrue with a value claim of 𝑆̄ =𝑉, the bidder will need to secure Suppose that absent the winning bidder’s project, the token price the same value of 𝑡 𝑓 by scaling 𝑅̄ , the surplus claim accompanying the would evolve as a random variable, 𝑊̃ 𝑏, the base outcome, and that the value claim 𝑆̄ =𝑉, by the factor 𝑆−𝑃 0. The bidder also will need to outcome of the winning bidder’s efforts changes the random variable to ( i a b 𝜙 n 1 n i ( d c 𝐷 t − r i d W c e 𝑣 e 𝑡 i a , 𝑑 e r p s 𝑃 ) a t e c ( 0 o t 𝑆 o , e t r m h 𝑆 d − e e , p a v 𝑉 𝑉 s l u a i u z t ) l ) e r u e 𝑞 > p e . t t l h h u ( d e 1 e s e a p s c − u l m o a r 𝑡 s i o p 𝑑 i m t u ) l u ( n l 𝑆 b o s t y s c o − s l . f a 𝑉 𝑆 𝑉 a T i − − m d h 𝑃 𝑃 ) d 𝑞 e 0 0 𝑅 e . 𝜙 𝑉 c d D ( o − r 𝐷 t n e e 𝑃 o q fi d 0 𝑣 k u , i n e t 𝑃 i e i n r o 0 e , 𝛿 n v d 𝑆 ( a 𝑆 i l i , n u n 𝑉 , e 𝑉 L t ) h e 𝑅 ) ̄ i m e n = t c m h o a 𝜙 a r a s t d ( e 𝐷 1 w e 𝑆 r 𝑣 a r , t e s > o 𝑃 q c 0 u 𝑉 l c a , i o 𝑆 r i v m e fo , e s 𝑉 e r r t d h t t ) h h i a − n e e t i i b h s 𝑊̃ c f i i i g a d g 𝑏 a h l h d l + t y h e o r i i 𝑊̃ g n 𝑊 u ’ ̃ s h t t 𝑒 o c 𝑒 e o o ff w 𝑊 w ̃ m u o h t i r 𝑏 e l c e t l . o r f i e B n m o s o u r 𝑊̃ e m t t 𝑊 ̃ 𝑒 o o a b r f 𝑒 s e i e . s 𝑊 o ̃ s T p t f t h h 𝑏 o r t o e e c h o d h e e p c u a ff c a e s c u o s t n t t i r r i d c v s t h a , e o i o l i s u l i f t y t n t o c t a h r i o c l n y s e m r d o e o e a e a f , m u p t i w D c e n i t n g A i g i t h d o O h v t n e a n , 𝐸 m t l t o t u ( h e k o 𝑊 e ̃ a e e , f n r n 𝑒 w e 𝑊 ̃ ) t p i = i h t 𝑏 r s h a i . c 𝑉 n t F e a o ∗ t s o h c r h − c o e i r e n s e 𝑃 w x t s a 0 o e a i t . r n q m e y T n u s p i y e f i n l o n n p e g r t - - , the case 𝑆=𝑉 assuming in both instances that the business plan results 𝑊̃ 𝑒, and its qualities, to the extent surmisable, are private information in token value 𝑉: of the bidder. These two random variables each contain both systemic and idiosyn- 𝑅= 𝑉 𝑆− − 𝑃 𝑃 0 0 [ 𝑅̄ +(1−𝑡 𝑏−𝑡 𝑓)(𝑆−𝑉)𝑞+𝛿(𝑆,𝑉) ] c c r a a n t n ic o t e l b e e m d e i n v t e s r . s T ifi h e e d m a a w rk a e y t , p b r u ic t e d s o s e y s s t n e o m t a p t r i i c c e ri s id k i c o o s m yn p c o r n at e i n c t r s i , s o k n , e w s h th ic a h t = 𝑉 𝑆− − 𝑃 𝑃 0 [ 𝑅̄ +(1−𝑡 𝑏)(𝑆−𝑉)𝑞+𝛿(𝑆,𝑉) ] − 𝑉 𝑆 − − 𝑃 𝑉 𝑅 c p a o n rt f b o e l io d . iversified away because it nets out to zero across the market 0 0 =𝑅̄ +(1−𝑡 𝑏)(𝑆−𝑉)𝑞+𝛿(𝑆,𝑉) case T s h . e O n id t e h n e t i o t n y e o h f a t n h d e , t w h i e n r n e i i n s g a b “b id a d re e r b o m n a e t s t ” e r e s n . tr C e o p n r s e i n d e e u r r t w w i o t h e l x i t m re it m ed e where the first step uses 𝑡 𝑓 = (𝑆− 𝑅 𝑃 0)𝑞 and the second step uses 1+ 𝑉 𝑆 − − 𝑃 𝑉 0 = r ri e s s k o u an rc d e s w a h n o d m w a e y a l h t a h v , e w d h i o ffi w c i u ll l t b y e f u u l n l a y b h le e d to gi d n i g v e sy rs s i t f e y m a a w ti a c y r i i d sk io . s T y h n e c r d a a t n ic - 𝑉 𝑆− − 𝑃 𝑃 0 0 . ger is that this entrepreneur will forgo undertaking a project with high social surplus because of the accompanying high risk and portfolio dis- With the required R in hand, the bid 𝐴that will produce the same tortions. 𝑃 am ) o 𝑞 u − nt 𝑅 ̄ of i s e : xpected bidder added token value as the bid 𝐴̄ =(1−𝑡 𝑏)(𝑉− priv O a n te t h eq e u o i t t h y e fi r r h m a s n , d o a r r v e e i n n t s u ti r t e u t c i a o p n i a ta l l i n fi v r e m st s o t r h s, a s t u e c x h is a t s i n a h pa ed rt g b e e f c u a n u d s s e , 0 they are vehicles to solve exactly these hedging and diversification prob- 𝐴=(1−𝑡 𝑏)(𝑆−𝑃 0 )𝑞− ( 𝑅̄ +(1−𝑡 𝑏)(𝑆−𝑉)𝑞+𝛿(𝑆,𝑉) ) l s e e m lv s e . s T a h r e e s e o w fi n rm ed s t b y y p i o c t a h l e ly r c in re v a e t s e t o p r o s, r t s f o o m lio e s t i o m f e i s n v la e r s g tm e e p n o t o s l s a n o d f t t h h e e m m - . and the change in the bid holding expected bidder added token value Idiosyncratic risks are thereby shifted to the broader investment sys- constant is: tem and can be diversified away. Systematic risk is absorbed by outside Δ𝐴=𝐴−𝐴̄ parties in the broader investment system hedging or adjusting their port- folios. We begin the analysis with the winning bidder being an institu- =−𝛿(𝑆,𝑉). tional investor and then consider the case of a bare bones entrepreneur. There are three separate elements of concern with respect to hedging and diversification for a winning bidder: (i) the token position consist- 108 The bidder can increase the resulting reduced bid by a small amount 𝜖if ing of 𝑡 𝑑 𝑞tokens; (ii) the value deposit liability; and (iii) and the surety there is a need to defeat a competing bid of exactly 𝐴∗. deposit liability. An institutional investor will simply absorb the token 2 29

J.Strnad Blockchain: Research and Applications 6 (2025) 100306 position. The idiosyncratic risk will be diversified away and the system- that business plan. A classic way to perform this kind of estimation is an atic risk shifted to appropriate parties through the broader investment event study. Khotari and Warner [78]pointed out that event studies can system. The institutional investor can focus purely on the question of be fairly accurate and robust in the short run but that they are unreliable choosing a business plan that maximizes social surplus creation, aligning in the long run, often failing to detect large effects at all in simulations, their motivation exactly with the auction mechanism. The determinis- much less determine their magnitude accurately. Thus, even if embody- tic analysis applies directly, interpreting 𝑉∗as an expected value rather ing event study methodology in a DAO were code feasible, it is not likely than a certainty. to be effective. It certainly would fall short of letting the bulk of the ad- The same expected value relationship does not apply for the value de- justments occur externally through institutional control parties shifting posit and surety deposit. These deposits function as derivatives positions risk to the general market, leaving only the relatively easy adjustments under the associated DAO Code rules. The value deposit is analogous to for the intrinsic option positions to the DAO Code. a bearish put spread, the analogy being exact in the case of the stan- We now turn to the opposite polar case in which the potential bid- dard token deposit forfeit function with no baseline loss penalty.109 der is a bare-bones entrepreneur instead of an institution that provides With respect to outcomes below 𝑃 0 , a large put position with appropri- flow through to the general investment market and has deep resources. ate strike prices would be required to offset potential forfeits involving We have highlighted the danger that the bare-bones entrepreneur may both the value deposit and surety deposit. The 𝑇 1 token holders, who choose to forgo a project with high social surplus due to unacceptably benefit if the deposits are forfeited in part or entirely by the control high risk. The entrepreneur also may need substantial funding to cover party, effectively hold all these derivatives positions. When the control the value and surety deposits as well as the cost of the business plan. party succeeds in bringing the token value up to 𝑉∗ in the determin- A classic market solution to these problems is to put the entrepreneur in istic setting, both deposits are fully refunded and the 𝑇 1 token holders a management role, with one or more institutional investors providing receive nothing. In a stochastic setting, 𝑉∗ is an expected value, not a the funds, and then to create a management contract that gives the en- certainty. There is a probability that the token price will never reach trepreneur incentives to choose and implement the highest value-added 𝑉∗ due to stochastic elements unrelated to the cogency of control par- project net of cost, where the cost itself is covered by investor funding. ty’s business plan and the effectiveness of execution of the plan. In that The investors are diversified and are not affected by idiosyncratic risk. case, the control party will lose part or all of the value deposit, and if In this context, Park and Vrettos [79]discussed the design of manage- the stochastic elements are strong enough on the downside to result in ment incentives through compensation contracts, summarized much of a token price below 𝑃 0 , part or all of the surety deposit. There is no the previous literature, and showed that a management contract that in- corresponding upside: The deposits are fully refunded if 𝑉∗ is reached cludes convex compensation such as call options is superior if it is set up on a sustained basis, but attaining a higher level than 𝑉∗ results in no with a diversified index as the baseline. Call options reward the manager additional benefit. The overall result is that in the stochastic case, the for achieving the high token values envisioned in the business plan and, implicit derivatives positions inherent in the two deposits both have a combined with salary and other stable elements, align the manager’s negative expected value for the winning bidder, while in the determin- financial returns with attaining success with the business plan. The di- istic case they had zero expected value. versified index baseline moves the focus of risk-taking to idiosyncratic As in the case of the token position, an institutional investor can pass risk, which is immune to manager hedging. Suitable levels of the call op- on the idiosyncratic risk and systematic risk associated with the implicit tion compensation will create the required incentives for the manager option positions arising from the deposit arrangements to the broader to fully execute on the business plan despite the attendant risks. investment system, which can eliminate the idiosyncratic risk and ab- sorb the systematic risk. But the institutional investor cannot avoid the References negative expected value hit associated with these positions, a hit that artificially lowers the appeal of surplus-creating business plans. Adjust- [1] P.Vigna,Chieflesscompanyrakesinmorethan$100million,http://www.wsj.com/ ment of the auction mechanism itself is required to address this problem. articles/chiefless-company-rakes-in-more-than-100-million-1463399393, 2016. 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