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Imperfect Commitment and the Revelation Principle
Abstract
We consider mechanism design problems with n agents when the mechanism designer cannot fully commit to an allocation function. With a single agent (n=1) optimal mechanisms can always be represented by direct mechanisms, under which each agent’s message set is the set of his possible types [Bester, H., Strausz, R., 2000. Contracting with imperfect commitment and the revelation principle: the single agent case. Free University of Berlin, mimeo]. We show that this result does not hold if n≥2. That is, in mechanism design problems with multiple agents the use of direct mechanisms may be suboptimal.
... 6 Bester and Strausz (2001) showed that the designer may optimally use a direct mechanism under which truthful revelation is an optimal strategy for the agent, but unlike in the case of the conventional revelation principle, the agent cannot use this strategy with probability one. This result extends to multiagent environments when only one agent is privately informed (see Evan and Reiche (2008)) but not to the case in which several agents have private information, like the one in our model (see Bester and Strausz (2000)). Dewatripont and Maskin (1990), and more recently Neeman and Pavlov (2012)). ...
... This result comes at no surprise in light of the existing literature on mechanism design with limited commitment. In particular, Bester and Strausz (2000) and Evans and Reiche (2008) highlighted the particular difficulty in restoring variants of the revelation principle in environments where more than one agent has private information, which is the case here. ...
... In fact, it is well known that in some settings the opposite is true. For example, Bester and Strausz (2000) showed that in a contracting problem, when there are multiple agents and the designer cannot fully commit to an allocation function, the optimal contract is sometimes achieved when the set of messages is strictly greater than the set of types and some types randomize. ...
We study intermediaries who seek to maximize gains from trade in bilateral negotiations. Intermediaries are players: they cannot commit to act against their objective function and deny, in some cases, trade they believe to be beneficial. This impairs their ability to assist the parties relative to conventional mechanisms. We analyze this limited commitment environment as a standard mechanism design problem with an additional “credibility” constraint, requiring that every outcome be interim‐optimal conditional on available information. We investigate how such intermediaries communicate with the parties, analyze the tradeoffs they face, and study the bounds on what they can achieve.
... As discussed in Section 4, we cannot guarantee downward-looking constraints bind at the optimum when there are three or more types. Bester and Strausz (2000) Bester and Strausz (2000) show that, with multiple agents, the result for the singleagent case in Bester and Strausz (2001) no longer holds. That is, if M " S and β is deterministic, then there are equilibria with mechanisms in which M ‰ V , whose payoffs cannot be replicated with canonical mechanisms. ...
... As discussed in Section 4, we cannot guarantee downward-looking constraints bind at the optimum when there are three or more types. Bester and Strausz (2000) Bester and Strausz (2000) show that, with multiple agents, the result for the singleagent case in Bester and Strausz (2001) no longer holds. That is, if M " S and β is deterministic, then there are equilibria with mechanisms in which M ‰ V , whose payoffs cannot be replicated with canonical mechanisms. ...
... The principal's payoffs are such that if, after seeing m, his posterior is µpmq, then he chooses allocation a˚pmq " 2p1´µpmqq. Bester and Strausz (2000) construct an equilibrium with three messages tm a , m b , m c u that cannot be replicated with messages tv, vu. Let M " tm a , m b , m c u. Then there is a PBE such that µpm a q " 1, µpm b q " 1{2, µpm c q " 0 a˚pm a q " 0, a˚pm b q " 1, a˚pm c q " 2. ...
We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.
... This is evident from the many existing acts and regulations whose goal is to guarantee that markets are not biased against certain groups in the population. 3 In the context of mechanism design, a natural candidate for an anti-discriminatory regulation is that the "rules of the game" are the same for all participants. In other words, the mechanism should be symmetric across agents. ...
... 570 (2013). 3 For example, the U.S. Equal Employment Opportunity Commission (EEOC) enforces several antidiscriminatory labor-market laws. Another example is the Genetic Information Nondiscrimination Act of 2008 in health insurance markets. ...
... This stands in stark contrast to the results for implementation in Bayes-Nash equilibrium. 6 Other examples that illustrate the potential importance of indirect mechanisms include [3] for the case where the designer lacks commitment power, [17] when agents have menu-dependent preferences, and [18] when only deterministic mechanisms are allowed. 7 The equilibrium used in the proof of Theorem 1 is focal in the sense that each agent reports his true name and type. ...
Designers of economic mechanisms can often benefit by using discriminatory mechanisms which treat agents asymmetrically. This paper studies the extent to which a policy prohibiting biased mechanisms is effective in achieving fair outcomes. Our main result is a characterization of the class of social choice functions that can be implemented by symmetric mechanisms. When the solution concept used is Bayes–Nash equilibrium, symmetry is typically not very restrictive and discriminatory social choice functions can be implemented by symmetric mechanisms. Our characterization in this case is based on a ‘revelation principle’ type of result, where we show that a social choice function can be symmetrically implemented if and only if a particular kind of (indirect) symmetric mechanism implements it. When implementation in dominant strategies is considered, only symmetric social choice functions can be implemented by symmetric mechanisms. We illustrate our results in environments of voting with private values, voting with a common value, and assignment of indivisible goods.
... The seller chooses prices in the durable goods case, and reservation prices in McAfee and Vincent (1997). 2 Skreta (2006b) examined the case where the seller faces one buyer whose valuation is private information in a …nite horizon model (essentially the durable good case) and showed that in fact posted prices are revenue maximizing among all possible conceivable mechanisms. It is interesting and relevant to characterize what is the revenue maximizing procedure when the seller faces many buyers. ...
... That paper establishes that for single agent and …nite type models it is without loss of generality to restrict attention to mechanisms with message spaces that have the same cardinality as the type space and where the agent reports his true type with strictly positive probability. However, as Bester and Strausz (2000) show this result fails with multiple agents. ...
... As we mentioned in the introduction, and is well understood by now, 13 when the mechanism designer behaves sequentially rationally, one cannot apply the standard revelation principle. Moreover, the extended revelation principle for environments with limited commitment by Bester and Strausz (2001), is not applicable in multi-agent environments, see Bester and Strausz (2000). ...
First (or second) price auctions with optimally chosen reserve prices maximize revenue among all possible selling procedures when buyers are risk-neutral, ex-ante identical, and the seller commits to throw away the object for sale if no one bids above the reserve price. However, sellers seldom remove unsold items from the market: Real estate, used cars and art reappear in later auctions. This paper derives the profit-maximizing selling procedure when the seller, after each unsuccessful attempt to sell the item, updates her information about the buyers’ willingness to pay and proposes an optimal selling procedure given the updated information. We show that first- (or second-) price auctions with optimally chosen reserve prices are revenue-maximizing when buyers are ex-ante identical. When buyers’ valuations are drawn from different distributions, the seller maximizes revenue by assigning the good to the buyer with the highest virtual valuation if it is above a buyer-specific reserve price. Reserve prices drop over time. How much the optimal reserve prices drop depends on how the seller discounts the future. Inability to commit is costly for the seller. The revenue loss is highest for intermediate values of the discount factor and when the number of buyers is small.
... a mediator than without, we will concentrate on the PBE that yields the principal the highest utility. 10 Due to a generalized revelation principle proven in Bester and Strausz (1998), we may without loss of generality assume that the message space corresponds to the set of types, i.e. M = I = f1; 2g. ...
... As soon as the optimal non{mediated contract involves partial information revelation, a mediator may improve outcomes. As shown in Bester and Strausz (1998) partial information revelation is a typical feature of mechanism design models with imperfect commitment (see also Hart and Tirole 1988and La ont and Tirole 1988,1990). ...
... This implies that the agent tells the truth with a strict positive probability, but, in contrast to the standard revelation principle, it may be optimal for the principal to let some type lie with a positive probability. For more details seeBester and Strausz (1998). ...
We study the effectiveness of mediators in situations of conflict. In a game of cheap talk a principal may employ a mediator whose task is to gather information and make non--binding proposals. We show that mediators facilitate information transmission and are helpful if and only if the likelihood of a conflict of interest is strictly positive but not too high. Mediation increases the amount of information that can be induced in equilibrium and is helpful when full information revelation is not feasible. The insights of this paper extend to general models of mechanism design with imperfect commitment of the contract designer.
... It is worthwhile to mention that mechanism design approaches considered in Szentes On the other hand, the class of mechanisms considered in Szentes (2010) and in this paper still allows a principal to commit to a mechanism that specifies the set of a principal's actions as a function of agents' messages sent to him. 4 ...
... Suppose that there is only one principal in a model. Given a mechanism γ 1 offered by principal 1 (i.e., single principal), a profile of continuation-equilibrium communication strategies c 1 (γ 1 ) induces a Bayesian incentive compatible direct mechanism g 1 according to(4) in which only agents send type messages and the principal does not send a message to himself. Therefore, the standard Revelation Principle holds. ...
This paper proposes a general competing mechanism game of incomplete information where a mechanism allows its designer to send a message to himself at the same time agents send messages. This paper introduces a notion of robust equilibrium. If each agent's payoff function is separable with respect to principals' actions, they lead to the full characterization of equilibrium allocations in terms of incentive compatible direct mechanisms without reference to the set of arbitrary mechanisms allowed in the game. Szentes' Critique (Szentes (2010)) on the standard competing mechanism game of complete information is also valid in a model with incomplete information.
... Bester and Strausz (2000) show that, with multiple agents, the result for the singleagent case in Bester and Strausz (2001) no longer holds. That is, if M " S and β is deterministic, then there are equilibria with mechanisms in which M ‰ V , whose payoffs cannot be replicated with canonical mechanisms. ...
... The principal's payoffs are such that if, after seeing m, his posterior is µpmq, then he chooses allocation a˚pmq " 2p1´µpmqq. Bester and Strausz (2000) construct an equilibrium with three messages tm a , m b , m c u that cannot be replicated with messages tv, vu. Let M " tm a , m b , m c u. Then there is a PBE such that µpm a q " 1, µpm b q " 1{2, µpm c q " 0 a˚pm a q " 0, a˚pm b q " 1, a˚pm c q " 2. ...
We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.
... ; with parametrizing the inverse Frisch elasticity. 31 Because these restrictions are not important for the qualitative results, in the discussion below I will specialize the notation to the above functional form only when presenting some numerical results. For a more general treatment of the problem in which (a) the agents live, and work, for arbitrarily long horizons, (b) agents are risk averse, (c) the planner has smoother aversion to inequality (captured by arbitrary q functions), (d) the agents' productivity evolves according to a general type process, I refer the reader to Makris and Pavan (2016). ...
... The optimality condition in (31), instead, combines the above static e¤ects with the dynamic e¤ects that a higher y 1 has on the principal's payo¤, net of the agents' informational rents. As discussed above, holding …xed the period-2 policies, as speci…ed in = hy; ci ; the term LD F B; ( 1 ) ...
This article was prepared for an invited session at the 2015 World Congress of the Econometric Society. Through a unifying framework, I survey recent developments in the dynamic mechanism design literature and then introduce two new areas that I expect will draw attention in the years to come: robustness and endogenous types.
... In this environment, the seller minimizes his losses by holding the initial auction with an elevated reserve and reducing the reserve with every subsequent auction. 4 In contrast, we find that a seller without commitment power can sustain an elevated reserve price provided that the quality of the match is sufficiently important to him. If the seller associates bids which fall below the reserve with a poor match and the adverse effect of a poor match is sufficiently large, then the seller will prefer retaining the contract to accepting a bid which does not meet the reserve. ...
... Che (1993) states that in the absence of commitment "the only feasible scoring rule is one that reflects the seller's [true] preference ordering," and Rezende (2004) allows a seller without commitment power to renege on the announced allocation rule and select the auction winner arbitrarily. Our representation is also consistent with the principalagent model in Bester and Strausz (2000): they define imperfect commitment in terms of a two-stage game, in which agents select messages in the first stage and the principal updates his beliefs and selects an allocation in the second stage. ...
In many auctions, matching between the bidder and seller raises the value of the contract for both parties. However, information about the quality of the match may be incomplete. We consider the case in which each bidder observes the quality of his match with the seller but the seller does not observe the quality of his matches with the bidders. Our objective is to determine whether it is in the seller's interest to observe the matches before selecting the winner. It is shown that the seller’s value for the information may be negative: the seller’s knowledge of the matches generates an asymmetry across bidders which depresses bids. The more matching matters, the greater the penalty associated with observing the matches.
... Due to a generalized revelation principle proven in Bester and Strausz (1998), we m a y without loss of generality assume that the message space c orresponds to the set of types, i.e. M = I = f1; 2g. ...
... This i m plies that agents tell the truth with a strict positive probability, but, in c o n trast to the standard revelation principle, it m a y b e o ptimal f or the principal to let the agents lie with some positive probability. F o r m ore details seeBester and Strausz (1998). ...
This paper offers a new type of explanation for economic institutions as playing the role of mediators in the sense of Myerson (1985) to facilitate communication in contracting settings with ex ante asymmetric information and limited commitment. It derives necessary and sufficient conditions under which mediation is strictly helpful and provides a straightforward, yet general intuition for this result. As an application of our idea we explain the widely observed use of consultants during the restructure of firms.
... Le principe de révélation 13 veut que le principal propose à l'agent un contrat de telle sorte que obtenant le maximum même dans les circonstances où il aurait intérêt à mentir, l'agent opte pour la vérité sur son type ou son niveau d'effort, etc. Le « contrat de dette standard » répond à ce principe : le banquier se contente d'un montant fixe et abandonne tout le surplus à l'entreprise lorsque le projet a réussi c'est-à-dire lorsque l'entrepreneur a intérêt à mentir ; par contre lorsque le projet a échoué, compte tenu de la limitation de responsabilité, l'entrepreneur dit la vérité et c'est le banquier qui fait 13 Selon Lim ( 2000) et Bester et Strausz (2004), les exposés de base du principe de révélation remontent à Gibbard (1973), Green et Laffont (1977), Myerson (1979) et Dasgupta, P., Hammond, P., Maskin, E., (1979) y Payoff (brut) … de l'Entrepreneur ...
Cet article fait une typologie des formes d'exécution des contrats financiers et explore la nature et les fondements des modes d'exécution. L'impossibilité de contraindre légalement les contrats éloigne de l'optimum social de premier rang. Cela peut être dû à la faiblesse des lois et de l'appareil judiciaire, mais souvent, même les systèmes judiciaires les plus parfaits ne peuvent pas conduire à l'optimum premier ; dans ces cas, seul un mode d'exécution informel peut améliorer la situation. Les modes d'exécution effectives disponibles dans une société influencent donc son architecture financière. Si la provision du type d'exécution exploitée par les institutions financières n'est pas appropriée à leur technologie, il en résultera une architecture sous-développée. Des institutions capables d'exploiter les types disponibles peuvent alors émerger. Pour perfectionner la qualité de la finance, il faudra donc non seulement emprunter la voie judiciaire, mais également promouvoir les contrats qui s'auto-exécutent. Transplanter l'architecture juridique des pays développés dans les pays en développement peut avoir des effets pervers. Abstract This article builds a typology of financial contract enforcement and explores the nature and the foundations of each type of enforcement. The impossibility of enforcement of the first best contracts leads to a second best. This situation is explained especially by the weakness of the law and of legal enforcement. The types of enforcement available in a society influence its financial architecture. If the provision of enforcement used by the financial institutions is not suitable to their technology, this will lead to underdeveloped financial architecture. Then institutions capable to exploit existing enforcement provision may emerge. To build sustainable finance, it's useful to use courts enforcement, but also type of self-enforcing contracts. The transplant effect of judiciary architecture of developed countries in developing country may be perverse.
... Indeed in this case no agent has an incentive to oppose a principal's decision to dissolve the pair, and the ability to commit becomes irrelevant. Under this condition, we show in Appendix C that a good equilibrium exists for a non-empty subset of parameters, despite the fact that the revelation principle does not hold (see Bester and Strausz 2000). ...
A large population of fixed-type agents engage in exclusive pairwise relationships in a decentralized setting. At the onset, agents randomly meet in pairs under private information of individual time-invariant types. They play a voluntary contribution game. At the end of the first period, members of each pair either stay together in the second period, in which case reported information is common knowledge, or quit and meet randomly new partners, under private information of individual types. Thus, either long-term or short-term relationships may arise. We show that there are values of the parameters such that information extracted in the first period has a positive effect on social efficiency. We give an interpretation of our results in terms of advantageous delegation of decisions to uninformed agents. Finally, we consider several extensions of the model in which our results still hold.
... A remarkable result, first noticed in Kumar (1985) and in Laffont and Tirole (1990) and then subsequently generalized in Bester and Strausz (2001), is that, with a single agent and finitely-many types, the maximal payoff for the principal can be attained by offering mechanisms in which the message space has the same cardinality as the type space, and by inducing the agent to report his true type with strictly positive probability. Unfortunately, as shown in Bester and Strausz (2000), in general, this result does not extend to settings with multiple agents. In the multi-agent environment in Skreta (2006), optimal allocations can be identified by restricting the seller to offering in period one a dynamic mechanism that is PBE-feasible. ...
The Introduction to the Symposium Issue on “Dynamic Contracts and Mechanism Design” of the Journal of Economic Theory provides an overview of the dynamic mechanism design literature. We then introduce the papers that are contained in the Symposium issue and finally conclude by discussing avenues for future research. Several of the papers contained in the Symposium issue were presented at the Economic Theory Workshop of the Cowles Foundation for Research in Economics at Yale University in June 2013.
... A remarkable result, first noticed in Kumar (1985) and in Laffont and Tirole (1990) and then subsequently generalized in Bester and Strausz (2001), is that, with a single agent and finitely-many types, the maximal payoff for the principal can be attained by offering mechanisms in which the message space has the same cardinality as the type space, and by inducing the agent to report his true type with strictly positive probability. Unfortunately, as shown in Bester and Strausz (2000), in general, this result does not extend to settings with multiple agents. In the multi-agent environment in Skreta (2006), optimal allocations can be identified by restricting the seller to offering in period one a dynamic mechanism that is PBE-feasible. ...
... Bester and Strausz (2001) show that a version of the Revelation Principle applies in situations when the principal without commitment faces only one agent. Their argument, however, does not extend to the multi-agent case (Bester and Strausz (2000)). In an infinite horizon setup with a continuum of agents, Acemoglu et al. (2006) show that the Revelation Principle holds on the equilibrium path, supported by the threat of agents reverting to not revealing any information after a deviation by the government. ...
How does the presence of financial markets shape the government's ability to implement social redistribution? Individuals typically do not constrain con-sumption to equal their net-of-tax income every period. Instead, access to financial markets allows them to allocate their resources over time. On the other hand, the markets that individual agents trade in are usually incom-plete in the sense that adjustments to contracts are costly. A mortgage, for example, helps to smooth housing-consumption. Yet, buying a house consti-tutes a significant individual commitment. It cannot costlessly be changed at every point in time, in particular a downward adjustment often comes with significant losses. Optimal redistributive policy ought to take agents' involve-ment in such financial markets into account. I study a two period endowment economy with heterogeneous income types and private information, where a government without commitment cannot provide any social redistribution. I show how agents' involvement in a financial market can improve the govern-ment's ability to commit at least to a partially separating allocation in the second period, enabling it to provide some redistribution across agents. In this world, agents borrow against their promised income and enter long-term indi-vidual consumption commitments. However, changing these contracts creates a deadweight loss. This changes the government's ex-post incentives to re-nege on the promised tax schedule and fully redistribute, because some agents would have to default on their loans. I show that whenever this default cost is positive, the government is able to commit to a schedule that only pools some agents of similar type together. In other words, it serves as a commitment device in the sense that it enables the government to commit to not exploit a limited amount of information. Thus, the presence of financial markets may in fact facilitate redistribution.
... Table 5 contains the correlation coefficient for the interest rate margin and collateral to loan ratios. 18 The negative and statistically significant value of Spearman's rho, ρ S , indicates that for the whole sample, higher collateral levels are closely associated 17 The credibility of this signal should be higher with concentrated ownership structure e.g. a sole proprietorship or two person partnership (see Bester and Strausz (2000)) for how multiple agents cloud the clarity and credibility of a signal 18 We only considered the borrowers who had borrowed at least £1,000 in our subsequent estimations in order to attenuate the risk of a trivial solution arising where the bank does not take collateral on very small with lower interest rates. This feature holds strongly in the case of the UK Personal, Property Investment, Non-Food Retail and Other sectors. ...
This paper uses unique data and augments existing theory focussing on bank's lending to new ventures. We are primarily concerned with banks' use of collateral and interest margins in terms of reducing adverse selection and moral hazard problems. We find a trade-off between interest margins and collateral per unit borrowed. Margins are insensitive to the magnitude of collateral per unit of borrowing but borrowers who post no collateral are associated with higher interest margins. Our theory and evidence suggests that liquidity constraints may be less prevalent at low borrower wealth than presupposed. We conclude that it is more the offering rather than the amount of collateral that matters to banks.
... 14 Therefore our methodology is applicable also to the case of multiple agents. This differs from the extension of the Revelation Principle for direct communication derived in Bester and Strausz [8], which does not hold for multiple agents (see [7]). The reason is that with direct communication the agent has to be indifferent between all messages that he selects with positive probability. ...
This paper provides new analytical tools for studying principal-agent problems with adverse selection and limited commitment. By allowing the principal to use general communication devices we overcome the literature's common, but overly restrictive focus on one-shot, direct communication. In addition, general communication devices solve two fundamental problems of contracting with imperfect commitment: First, they allow us to identify the ‘local downward’ incentive constraints as the relevant ones if the agent's preferences satisfy a single-crossing property. Second, we show how one may restrict the cardinality of the message spaces of the communication device. An example illustrates our arguments and the suboptimality of one-shot, direct communication.
... As for transferable utility however, the extension is not straightforward, as the generalized revelation principle need not hold for multiple agents (see Bester/Strausz (2000)). ...
The paper studies the role of delegation and authority in a principal-agent relation in which a non-contractible action has to be taken. The agent has private information relevant for the principal, but has policy preferences different from the principal. Consequently, an information revelation problem arises. I consider a partially incomplete contracting environment with contractibility of messages and decision rights and with transferable utility. I contribute to the literature by allowing for message-contingent delegation and by deriving the optimal partially incomplete contract. It is shown that message-contingent delegation creates incentives for information revelation and may outperform unconditional authority and unconditional delegation.
... The idea that the mechanism should not reveal too much information is well known in multistage games with private information and hidden actions: Too much information makes it easier for agents to manipulate the mechanism. 1 In my paper, an agent who learns that his counterparty has already entered a contract believes that his counterparty plans a strategic default. Hence, the agent cannot precommit to enter a contract with such a counterparty. ...
When contracts are unobserved (and nonexclusive), agents can promise the same asset to multiple counterparties and subsequently
default. I show that a central mechanism can extract all relevant information about contracts that agents enter by inducing
them to report one another. The mechanism sets position limits and reveals the names of agents who hit the limits according
to (voluntary) reports from their counterparties. This holds even if sending reports is costly and even if agents can collude.
In some cases, an agent’s position limit must be nonbinding in equilibrium. The mechanism has some features of a clearinghouse.
... However, Forges' solution is unapplicable here: in the auction scenario the set of posteriorly optimal mechanisms would typically be empty. 6 Veto-incentive compatibility = incentive compatibility + individual rationality after all histories (e.g. Forges, 1998). ...
We study auction design when parties cannot commit themselves to the mechanism. The seller may change the rules of the game and the buyers choose their outside option at all stages. We assume that the seller has a leading role in equilibrium selection at any stage of the game. Stationary equilibria are characterized in the language of vonNeumann-Morgenstern stable sets. This simplifies the analysis remarkably. In the one buyer case, we obtain the Coase conjecture: the buyer obtains all the surplus and efficiency is reached. However, in the multiple buyer case the seller can achieve more: she is able to commit to the English auction. Typically the converse also holds, the English auction is the only stable auction mechanism.
Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper we rationalize the adoption of such seemingly sub-optimal bidding within the canonical quasi-linear framework. The crux of the argument lies in the notion of *commitment*. We consider a multi-stage game where first the auctioneer declares the auction rules; then bidders select either the tCPA or mCPA bidding format and then, if the auctioneer lacks commitment, it can revisit the rules of the auction (e.g., may readjust reserve prices depending on the observed bids). Our main result is that so long as a bidder believes that the auctioneer lacks commitment to follow the rule of the declared auction then the bidder will make a higher profit by choosing the tCPA format over the mCPA format. We then explore the commitment consequences for the auctioneer. In a simplified version of the model where there is only one bidder, we show that the tCPA subgame admits a *credible* equilibrium while the mCPA format does not. That is, when the bidder chooses the tCPA format the auctioneer can credibly implement the auction rules announced at the beginning of the game. We also show that, under some mild conditions, the auctioneer's revenue is larger when the bidder uses the tCPA format rather than mCPA. We further quantify the value for the auctioneer to be able to commit to the declared auction rules.
Integrating Cost Reduction and Supplier Selection Activities
Manufacturers who outsource production may find ways to reduce suppliers’ cost to lower the contract price. Conventionally, this is done after supplier selection. However, in practice, a sizable portion of the degree to which the manufacturer can help a supplier reduce cost could be learned before the supplier starts production. This opens up a possibility to better integrate supplier selection and cost-reduction activities. In “Procurement Mechanisms with Postauction Preaward Cost-Reduction Investigations,” Chen, Beil, and Duenyas explore an alternative procurement process wherein, after suppliers’ initial pricing bids are collected, the manufacturer investigates suppliers’ cost-saving potential and then leverages this information to select the contract winner. They provide analytical and numerical evidence that this integrated procurement process not only helps the manufacturers reduce cost significantly, but also benefits the suppliers in many plausible scenarios.
This paper studies a general competing mechanism game of incomplete information where each seller can offer a contract that determines a menu of any complex mechanisms conditional on buyers’ messages, and then chooses a mechanism that he wants from the menu. The focus is the class of robust equilibria in which sellers punish a deviating seller with dominant strategy incentive compatible direct mechanisms. We show how to characterize the class of such equilibria. In applications, the number of sellers is endogenized given a number of buyers and fixed entry costs. In a large market, a seller’s equilibrium ex-ante expected net profit is always equal to zero but any price in an interval can be supported as an equilibrium price. The equilibrium ratio of the number of buyers to the number of sellers is lowest at the monopoly price, and increases as the price moves farther away from it in either direction.
We study sender-receiver games in which a privately informed sender sends a message to N receivers, who then take an action. The sender’s type space T has finite cardinality (i.e., |T|<∞). We show that every equilibrium payoff vector (resp. every Pareto efficient equilibrium payoff vector) is achieved by an equilibrium in which the sender sends at most |T|+N (resp. |T|+N−1) messages with positive probability. We also show that such bounds do not exist when two privately informed senders simultaneously send a message to a receiver.
I consider a scenario where a social planner suspects that a crime has been committed. There are many suspects and at most one of them is guilty. I characterize the optimal mechanism for the social planner under different assumptions with respect to her commitment power. I find that the optimal mechanism is a “confession inducing mechanism”: before an investigation, each agent can confess to being guilty in exchange for a reduced punishment. I find that these mechanisms do better than the traditional trial mechanism because of information externalities: when an agent credibly confesses his guilt, he reveals everyone else's innocence.
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We consider a firm that solicits bids from a fixed-sized pool of yet-to-be-qualified suppliers for an indivisible contract. The contract can only be awarded to a supplier who passes a multistage qualification process. For each stage of the qualification process, the buyer incurs a fixed testing cost for each supplier she chooses to test. The buyer seeks an optimal mechanism—that is, one that minimizes her total expected cost. Motivated by the buyer’s urgency (or the lack of it) of time for completing the qualification process, we obtain optimal mechanisms for two testing environments: (1) simultaneous testing, where in each stage, the buyer selects a subset of those suppliers who have passed all the previous stages and tests them simultaneously; and (2) nonsimultaneous testing, where the simultaneous-testing requirement is not imposed. Under simultaneous testing, the admission policy for selecting suppliers at each stage is based on nonuniform reserve-price thresholds. Under nonsimultaneous testing, too, the admission policy is threshold based, but the selection process is sequential in nature. The relative increase in cost due to the simultaneous-testing requirement is (under a mild condition) monotonically increasing in the number of suppliers, the expected multistage testing cost, and the overall passing probability. We also study the optimal sequencing of the qualification stages and show that the buyer should schedule the stages in increasing order of the ratio of their testing cost to their failing probability. Finally, for the simpler setting of a single-stage qualification process and a single supplier, we study a two-dimensional mechanism design problem where, in addition to cost, the passing probability is also private to the supplier. Here, too, threshold-based admission remains optimal, and the buyer offers either a pooling or a separating contract.
The online appendix is available at https://doi.org/10.1287/msom.2017.0664 .
We consider a newsvendor who earns a revenue from the sales of her product to end users as well as from multiple advertisers paying to obtain access to those end users. We study the optimal decisions of a price-taking and a price-setting newsvendor when the advertisers have private information about their willingness to pay. We focus on the impact of the number of advertisers on the newsvendor’s optimal decisions. We find that regardless of the number of advertisers, the newsvendor may exclude advertisers with a low willingness to pay and distort the price and inventory from their system-efficient levels to screen the advertisers. Moreover, the newsvendor’s decision to exclude an advertiser is based exclusively on that advertiser’s characteristics, and the newsvendor’s optimal decision thus reveals independence among the advertisers. Nonetheless, the profits of the newsvendor and the advertisers also display network effects as both increase in the number of advertisers. Finally, our numerical results show that the newsvendor prefers an equivalent single advertiser to multiple advertisers due to the pooling effect.
The paper presents a formal model of the exit and voice framework proposed by Hirschman (14). To be more precise, we modify the cheap talk model of Crawford and Sobel (9) such that the sender of a cheap talk message has the exit option. We demonstrate that the existence of the exit option may increase the informativeness of cheap talk and improve welfare if the dierence between the sender's maximum stay payo and exit payo is comparatively small. Moreover, it is verified that perfect information transmission can be approximated as the dierence goes to zero. The results suggest that the exit reinforces the voice in that the credibility of the exit increases the informativeness of the voice.
Suppose a principal can only sign public bilateral contracts with agents who have private information on their costs of producing goods on his behalf. The principal may manipulate what he learns by contracting with an agent when dealing with others. Introducing this possibility significantly simplifies optimal mechanisms. It restores both the continuity of the princi-pal's and the agents' payoffs and that of the optimal mechanism with respect to the correlation in the agents' types. Correlation remains useful to bet-ter extract the agents' information rent even though it no longer allows full extraction. In private values contexts, a Revelation Principle with bilateral contracting identifies the set of implementable allocations by means of sim-ple non-manipulability constraints. Equipped with this tool, we characterize optimal non-manipulable mechanisms in various environments. Those mech-anisms trade off the marginal benefit of production against some generalized virtual costs whose expressions generalize that found at zero correlation.
In contracting games where multiple principals interact with a common agent, standard revelation mechanisms have been shown to be inadequate to characterize the set of equilibrium allocations. This paper introduces a Markovian Revelation Principle for common agency games which establishes that any contractual relationship between a principal and an agent can be reduced to a probability distribution over a set of payoff-relevant decisions. By restricting attention to Markovian direct revelation mechanisms in which the agent truthfully reports to each principal his extended type, i.e. his exogenous private information along with the decisions contracted with the other principals, it is possible to replicate the entire set of equilibrium allocations that can be sustained by any profile of indirect mechanisms with arbitrary communication spaces. participants at the 2001 European Meeting and the 2002 North American Winter Meeting of the Econometric Society for discussions and useful suggestions. A special thank is due to Mike Peters who indicated several improvements upon a previous draft. We are also grateful to Allan Collard-Wexler who provided excellent research assistance. As usual, all errors remain our own.
This paper studies information transmission between multiple agents with di¤erent preferences and a welfare maximizing decision maker who chooses the quality or quantity of a public good (e.g. provision of public health service; carbon emissions policy; pace of lectures in a classroom) that is consumed by all of them. Communication in such circumstances su¤ers from the agents' incentive to "exaggerate" their preferences relative to the average of the other agents, since the decision maker's reaction to each agent's message is weaker than in one-to-one communication. As the number of agents becomes larger the quality of information transmission diminishes. The use of binary messages (e.g. "yes" or "no") is shown to be a robust mode of communication when the main source of informational distortion is exaggeration.
This article applies mechanism design to the study of international conflict resolution. Standard mechanisms in which an arbitrator
can enforce her decisions are usually not feasible because disputants are sovereign entities. Nevertheless, we find that this
limitation is inconsequential. Despite only being capable of making unenforceable recommendations, mediators can be equally
effective as arbitrators. By using recommendation strategies that do not reveal that one player is weak to a strong opponent,
a mediator can effectively circumvent the unenforceability constraint. This is because these strategies make the strong player
agree to recommendations that yield the same payoff as arbitration in expectation. This result relies on the capability of
mediators to collect confidential information from the disputants, before making their recommendations. Simple protocols of
unmediated communication cannot achieve the same level of ex ante welfare, as they preclude confidentiality.
In many auctions, a good match between the bidder and seller raises the value of the contract for both parties although information about the quality of the match may be incomplete. This paper examines the case in which the bidder is better informed about the quality of his match with the seller than the seller is. We derive the optimal mechanism for this setting and investigate whether the seller requires commitment power to implement it. It is shown that once the reserve price is set, it is optimal for the seller to do away with any matching considerations and allocate the contract on the basis of price alone. If matching is sufficiently important to the seller, the optimal mechanism may be implemented without commitment. However, if matching is not sufficiently important, the seller suffers a loss when he is unable to commit. The magnitude of this loss increases as the importance of matching decreases.
Bielefeld, University, Diss., 2005 (Nicht für den Austausch).
This paper briefly and informally surveys different theoretical models of relative concerns and their relation to inequality. Models of inequity aversion in common use in experimental economics imply a negative relation between inequality and happiness. In contrast, empirical studies on happiness typically employ models of relative concerns that assume that increases in others’ income always have a negative effect on own happiness. However, in these latter models, the relation between inequality and happiness can be positive. One possible solution is a rivalry model where a distinction is made between endowment and reward inequality which have respectively a negative and positive effect on happiness. These different models and their contrasting results may clarify why the empirical relationship between inequality and happiness has been difficult to establish.
Self-reporting of compliance status has become a common feature in the enforcement of environmental regulation. In this paper,
I generalize existing models of enforcement with self-reporting to include the possibility of private enforcement of regulation
through citizen suits. This allows me to identify an additional argument for the efficiency of self-reporting: it can increase
the likelihood of a successful suit and thus facilitate private enforcement of regulation. Specifically, if self-reporting
sufficiently increases the expected penalty for losing a citizen suit, if the costs of private enforcement are low, and if
inspection costs are high enough relative to enforcement costs, self-reporting lowers expected regulatory and social costs
by allowing the regulator to rely on private enforcement and decrease his enforcement efforts.
This paper extends the revelation principle to environments in which the mechanism designer cannot fully commit to the outcome induced by the mechanism. We show that he may optimally use a direct mechanism under which truthful revelation is an optimal strategy for the agent. In contrast with the conventional revelation principle, however, the agent may not use this strategy with probability one. Our results apply to contracting problems between a principal and a single agent. By reducing such problems to well-defined programming problems they provide a basic tool for studying imperfect commitment.
Bester and Strausz (2000) showed that the revelation principle of Bester and Strausz (2001) does not apply in a setting of many agents and no commitment. In their counterexample only one agent has private information. We show that if the parties can make ex ante transfers the revelation principle does extend to this setting. However, we show that it does not extend
to a setting in which more than one agent has private information.
Bester and Strausz (2000) showed that the revelation principle of Bester and Strausz (2001) does not apply in a setting of many agents and no commitment. In their counterexample only one agent has private information. We show that if the parties can make ex ante transfers the revelation principle does extend to this setting. However, we show that it does not extend to a setting in which more than one agent has private information.
In the absence of commitment to auditing, we study the optimal auditing contract when collusion between an agent and an auditor is possible. We show that the auditor can be totally useless if the auditor's independence can be compromised with relative ease. Even very stiff sanctions on fraud will be unable to make auditing optimal. We then derive a demand for independent external auditing. We endogenize collusion cost as the cost from the risk of future detection. We also derive a justification for the focus of the recent audit reforms on penalties on CEOs in cases of audit fraud. Copyright Blackwell Publishing Ltd. 2006.
This paper studies information transmission subject to anonymity requirements and communication in public good provision without transfers. The structure of informative equilibria under anonymity or in public good provision can di¤er substantially from that of direct one-to-one communication, and in particular we distinguish i) informational distortion caused by the intrinsic divergence of preferences between the decision maker and each agent; and ii) informational distortion caused by the decision maker's weak response to each agent's message due to the equal treatment of all agents that results from anonymity or the nature of public goods. We examine the interaction between these two types of distortion and demonstrate that they may partly offset one another. Information transmission and welfare can be enhanced by introducing the second type of distortion through anonymity when the first type of distortion is severe. In public good provision where the intrinsic preference divergence between the utilitarian decision maker and each agent is absent, as the number of agents becomes larger the quality of communication diminishes and informative equilibria converge to the one that can be played by letting each agent report a binary message (e.g. "yes" or "no") even if their preferences and the decision are continuous.
This paper constructs a two-country (Home and Foreign) general equilibrium model of Schumpeterian growth without scale effects. The scale effects property is removed by introducing two distinct specifications in the knowledge production function: the permanent effect on growth (PEG) specification, which allows policy effects on long-run growth; and the temporary effects on growth (TEG) specification, which generates semi-endogenous long-run economic growth. In the present model, the direction of the effect of the size of innovations on the pattern of trade and Home’s relative wage depends on the way in which the scale effects property is removed. Under the PEG specification, changes in the size of innovations increase Home’s comparative advantage and its relative wage, while under the TEG specification, an increase in the size of innovations increases Home’s relative wage but with an ambiguous effect on its comparative advantage.
As was shown by Dewatripont, optimal long-term contracts are generally not sequentially optimal. The parties ex-post renegotiate them to their mutual advantage. This paper fully characterizes the equilibrium of a simple two-period procurement situation and studies the extent to which renegotiation reduces ex-ante welfare: i) A central result is that, like in the non-commitment case, the second period allocation is optimal for the principal conditionally on his posterior beliefs about the agent. ii) The first period allocation exhibits an increasing amount of pooling when the discount factor grows. iii) With a continuum of types, it is never optimal to induce full separation. The paper also analyzes whether renegotiated long-term contracts yield outcomes resembling those under either unnegotiated long-term contracts or a sequence of short-term contracts and it links the analysis with the multiple unit durable good monopoly problem.
Consider a long-term relationship between a seller and a buyer whose valuation (for a per-period service or a durable good)
is private. As trade progresses, the valuation will be partially revealed, and it may be impossible for the parties to commit
ex-ante not to take advantage of this. We analyse this situation first by supposing that the parties can sign a sequence of
short-term contracts; and secondly by supposing that they can sign a long-term contract, but cannot commit not to renegotiate
it later. We find a close relationship in the second case between the optimal long-term contract and the non-commitment outcome
in the standard Coasian durable good model. Our results also have implications for hidden-information principal-agent models.
This paper extends the revelation principle to environments in which the mechanism designer cannot fully commit to the outcome induced by the mechanism. We show that he may optimally use a direct mechanism under which truthful revelation is an optimal strategy for the agent. In contrast with the conventional revelation principle, however, the agent may not use this strategy with probability one. Our results apply to contracting problems between a principal and a single agent. By reducing such problems to well-defined programming problems they provide a basic tool for studying imperfect commitment.
Collective choice problems are studied from the Bayesian viewpoint. It is shown that the set of expected utility allocations which are feasible with incentive-compatible mechanisms is compact and convex, and includes the equilibrium allocations for all other mechanisms. The generalized Nash solution proposed by Harsanyi and Selten is then applied to this set to define a bargaining solution for Bayesian collective choice problems.
Social decision mechanisms that admit dominant strategies and result in Pareto optima are characterized by the class of mechanisms proposed by Groves. The concept of decision mechanisms is generalized and the characterization is shown to extend to these cases.
It has been conjectured that no system of voting can preclude strategic voting--the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of voting in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a game form is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy.
As was shown by Dewatripont, optimal long-term contracts under asymmetric information are generally not time-consistent. This
paper fully characterizes the equilibrium of a two-period procurement model with commitment and renegotiation. It also analyzes
whether renegotiated long-term contracts yield outcomes resembling those under either unrenegotiated long-term contracts or
a sequence of short-term contracts, and links the analysis with the multiple unit durable good monopoly problem.
Contract renegotiation and coasian dynamics Characterization of satisfactory mechanisms for the revelation of preferences
- O Hart
- J Tirole
Hart, O., Tirole, J., 1988. Contract renegotiation and coasian dynamics. Review of Economic Studies 55, 509–540. Green, J., Laffont, J.-J., 1977. Characterization of satisfactory mechanisms for the revelation of preferences. Econometrica 45, 427–438
The implementation of social choice rules
- P Dasgupta
- P Hammond
- E Maskin
Dasgupta, P., Hammond, P., Maskin, E., 1979. The implementation of social choice rules. Review of Economic Studies 46,
185-216.
The implementation of social choice rules
- Dasgupta