Payoff equivalence between Bayesian and ex post individually rational dominant strategy mechanisms

Summary. An efficient, interim individually rational, ex post budget balanced Bayesian mechanism is shown to be payoff equivalent to an ex post individually rational and ex ante budget balanced dominant strategy mechanism. This result simplifies the search for mechanisms that implement efficient allocation rules by pointing to a class of Groves mechanisms. It eliminates the strict requirement of common knowledge of priors and can be applied to many problems of incomplete information. Received: October 22 1996; revised version: November 25, 1997     

Revelation of preferences for public goods: Aggregation by Abelian operations

When the utility functions for the public and private goods are additively separable, in the two-public-alternative situation, a new class of incentive compatible mechanisms is presented, and some of its properties are explored. If there are more than two public alternatives and if the utility functions remain separable according to a generalized addition (called an abelian operation), it is also possible to construct incentive compatible mechanisms. Such mechanisms are similar to those of Groves but they do not involve maximizing a sum of utilities.     

The robustness of the independent private value model in Bayesian mechanism design

Summary. In a Bayesian model of group decision-making, dependence among the agents' types has been shown to have a beneficial effect on the design of incentive compatible mechanisms that achieve the efficient choice associated with complete information. This effect is shown here to depend as much upon the use of large monetary transfers among the agents as it does upon dependence: if the transfers are bounded in magnitude, then nonexistence in the case of independence of an efficient, incentive compatible, ex ante budget-balanced and interim individually rational mechanism is robust to the introduction of a small amount of dependence among types. This robustness result supports the use of the simplifying assumption of independence in mechanism design. Received: October 28, 1996; revised version: May 28, 1997     

Equilibrium Selection and Stability for the Groves Ledyard Mechanism

In their seminal paper Groves and Ledyard (1976) construct a balanced incentive compatible mechanism that solves the free rider problem. In subsequent research, Bergstrom, Simon, and Titus (1983) prove that there exist numerous asymmetric equilibria in addition to the symmetric equilibrium. In the present paper, we explicitly solve for the additional equilibria and use computational experiments to examine the structure and stability of the set of equilibria of the Groves Ledyard Mechanism. We find that all of the equilibria found by Berstrom, Simon, and Titus are unstable and that for a high level of the punishment parameter these equilibria do not exist. Further, we find that there exists an additional boundary equilibrium for each of the equilibria found by Bergstrom, Simon, and Titus. The boundary equilibria are all stable.     

Mechanisms for a spatially distributed market

We consider the problem of a spatially distributed market with strategic agents. A single good is traded in a set of independent markets, where shipment between markets is possible but costly. The problem has previously been studied in the non-strategic case, in which it can be analyzed and solved as a min-cost-flow problem. We consider the case where buyers and sellers are strategic. Our first result gives a double characterization of the VCG prices, first as distances in a certain residue graph and second as the minimal (for buyers) and maximal (for sellers) equilibrium prices. This provides a computationally efficient, individually rational and incentive compatible welfare maximizing mechanism. This mechanism is, necessarily, not budget balanced and we also provide a budget-balanced mechanism (which is also computationally efficient, incentive compatible and individually rational) that achieves high welfare. Finally, we present results for some extensions of the model.     

Announcement or Contribution? The Relative Efficiency of Manipulated Lindahl Mechanisms

The private provision mechanism is individually incentive compatible but inefficient. The Lindahl mechanism is efficient but not incentive compatible. We analyze the outcome of the manipulated Lindahl mechanism. When the demand announcements of participants are unrestricted the Lindahl mechanism suffers from multiple equilibria. If the government removes the multiplicity by restricting the functional form of announcements the resulting Lindahl equilibrium can be made approximately efficient. Approximate efficiency is achieved by announcements that are one-dimensional regardless of the number of participants in the mechanism. This is in contrast to mechanisms that achieve exact efficiency but require announcements whose dimensionality increases at the same rate as the number of participants. The mechanism we describe benefits from simplicity at the cost of approximate efficiency. We demonstrate that mechanisms in which a linear demand function is announced are supermodular so play will converge to the Nash equilibrium for a range of learning dynamics.     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Ex ante efficiency implies incentive compatibility

We show that when agents become informationally negligible in a large economy with asymmetric information, every ex ante efficient allocation must be incentive compatible. This means that any ex ante core or Walrasian allocation is incentive compatible. The corresponding result is false for fixed finite-agent economies with asymmetric information. An example is also constructed to show that the ex post version of the result does not hold. Furthermore, we show that the result is sharp in the sense that it will fail to hold if one relaxes any of the main assumptions, namely, strong conditional independence on the information structure, strict concavity on the utility functions, type independence on the utility functions and endowments.      

Public goods with congestion

I consider the problem of the efficient provision of a congested (limited capacity) public good in a setting with asymmetric information. I show, in particular, that when the capacity of the good is limited, in a wide class of economies it is possible to construct an incentive compatible mechanism that always produces the good at the efficient level, balances the budget and satisfies voluntary participation constraints. This result is in contrast with the corresponding impossibility result for pure public goods due to Mailath and Postlewaite (Rev. Econ. Stud. 57 (1990) 351-359) and Rob (J. Econ. Theory 47 (1989) 307-333).     

Efficiency versus optimality in procurement

We study procurement procedures that simultaneously determine the specification and price of a good. Suppliers can offer and produce the good in either of two possible specifications, both of which are equally good for the buyer. Production costs are interdependent and unknown at the time of bidding. Each supplier receives two signals about production cost, one per specification. Our model is a special case of the interdependent value settings with multidimensional types in Jehiel and Moldovanu (Econometrica 69:1237–1259, 2001) where an efficient and incentive compatible mechanism exists. We characterize equilibrium bidding behavior if the winning supplier is selected purely on the basis of price, regardless of the specification offered. While there is a positive chance of obtaining an inefficient specification, this procurement mechanism involves lower information rents than efficient mechanisms, suggesting that there is a trade-off between minimizing expected expenditure for the good, and ensuring that the efficient specification is chosen.     

On the uniqueness of Groves mechanisms and the payoff equivalence principle

Consider a standard mechanism design setting with quasi-linear preferences and private valuations. From Holmström (1979), we know that if the valuations are smooth with respect to types then any efficient, dominant strategy mechanism is in the class of Groves mechanisms. Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms. This condition, which imposes a restriction on the behavior of the one-sided directional derivatives of the valuation functions with respect to individual types, is also shown to be sufficient and necessary to obtain the Payoff Equivalence principle for dominant strategy mechanisms whose choice rules are affine maximizers.     

Incentives in market games with asymmetric information: the core

Summary. This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players' strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core. Received: December 26, 2001; revised version: June 11, 2002 RID="*" ID"*" This work was financed, in part, by contract No 26 of the programme “P?le d'attraction interuniversitaire” of the Belgian government, and, in part, by research grant SBR93-09854 from the U.S. National Science Foundation. Much of my thinking about this topic was developed during a wonderful visit to CORE for the 1991–1992 academic year (on sabbatical from the University of Pennsylvania). This paper was originally circulated in December 1991 as CARESS Working Paper #91-38, Center for Analytic Research in Economics and the Social Sciences, Department of Economics, University of Pennsylvania and in February 1992 as CORE Discussion Paper 9221, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. RID="*" ID="*" At the very start of my research, Jean-Fran?ois Mertens was almost a co-author. Fran?ois Forges provided detailed comments at a later stage, during my visit to THEMA, Université Cergy-Pontoise, in Spring 1997. They are entitled to the customary disclaimer.     

The ABC mechanism: an incentive compatible payoff mechanism for elicitation of outcome and probability transformations

When it comes to experiments with multiple-round decisions under risk, the current payoff mechanisms are incentive compatible with either outcome weighting theories or probability weighting theories, but not both. In this paper, I introduce a new payoff mechanism, the Accumulative Best Choice (“ABC”) mechanism that is incentive compatible for all rational risk preferences. I also identify three necessary and sufficient conditions for a payoff mechanism to be incentive compatible for all models of decision under risk with complete and transitive preferences. I show that ABC is the unique incentive compatible mechanism for rational risk preferences in a multiple-task setting. In addition, I test empirical validity of the ABC mechanism in the lab. The results from both a choice pattern experiment and a preference (structural) estimation experiment show that individual choices under the ABC mechanism are statistically not different from those observed with the one-round task experimental design. The ABC mechanism supports unbiased elicitation of both outcome and probability transformations as well as testing alternative decision models that do or do not include the independence axiom.

     

Adverse selection under ignorance

Summary. We examine an adverse selection relationship in which the principal may ignore the ex ante distribution of the agent's types. The principal's behavior is described by a disutility function that covers the standard minimax regret and minimax loss criteria. We show that the incentive compatible and individually rational mechanism, which minimizes the maximal (or the minimal) principal's disutility over a set of priors, requires the efficient agents to realize the corresponding first-best actions and may demand actions lower than the first-best ones from less efficient agents. We also analyze the qualitative differences between the case in which the principal considers regrets and the case in which he considers losses. Received: 19 October 1998; revised version: 9 November 1999     

Incentive Contracts for Infrastructure,Litigation and Weak Institutions

In this paper we revisit incentive contract design in a simple setting, after developing a model that captures the fact that in weak institutional settings the procurement of large scale public works through contracts with strong incentives for private firms, may result in excessive litigation over contract terms. This result is possible because we assume that parties in litigation can influence (by purchasing better or more legal services) the observable merits of their case. In weak institutional settings, governments have an inherent disadvantage in these litigation contests. We show that a commitment to a prespecified level of litigation effort by the government, together with weaker incentive contracts, is a more efficient procurement mechanism.Jel Classification: D8, H57, H54, K41, K23, L51     

The Dynamic Vickrey Auction

We study the efficient allocation of a single object over a finite time horizon. Buyers arrive randomly over time, are long-lived, and have independent private values. The valuation of a buyer may depend on the time of the allocation in an arbitrary way. We construct an incentive compatible mechanism in which (A) there is a single financial transaction (with the buyer), (B) ex-post participation constraints are fulfilled, (C) there is no positive transfer to any agent and (D) payments are determined online. We exploit that under the efficient allocation rule, there is a unique potential winning period for each buyer. This reduces the multidimensional type to one dimension and the payment of the winner can be defined as the lowest valuation for the potential winning period, with which the buyer would have won the object. In a static model, this payment rule coincides with the payment rule of the Vickrey Auction.     

Optimal contract mechanisms for principal-agent problems with moral hazard and adverse selection

Summary We examine the problem of incentive compatibility and mechanism design for incomplete information principal-agent problems. Allowing for risk aversion on the part of the principal and agent, we show the existence of an optimal, incentive compatible contract selection mechanism for the principal under conditions of moral hazard and adverse selection. Since we assume that the contract set is a function space of state contingent contracts, and that the set of agent types is uncountable, the set of contract selection mechanisms becomes infinite dimensional. Hence, novel existence arguments are required. Our existence result extends those of Grossman and Hart [10] and Page [23] to an infinite dimensional setting with incomplete information.     

Ascending price Vickrey auctions

We show that an ascending price auction for multiple units of a homogeneous object proposed by Ausubel (i) raises prices for packages until they reach those nonlinear and non-anonymous market clearing prices at which bidders get their marginal products and (ii) the auction is a primal–dual algorithm applied to an appropriate linear programming formulation in which the dual solution yields those same market clearing prices. We emphasize the similarities with efficient incentive compatible ascending price auctions to implement Vickrey payments when there is a single object or when objects are heterogeneous but each buyer does not desire more than one unit. A potential benefit of these common threads is that it helps to establish the principles upon which Vickrey payments may be implemented through decentralized, incentive compatible procedures.     

Merger negotiations and ex-post regret

We consider a setting in which two potential merger partners each possess private information pertaining both to the profitability of the merged entity and to stand-alone profits, and we investigate the extent to which this private information makes ex-post regret an unavoidable phenomenon in merger negotiations. To this end, we consider ex-post incentive compatible mechanisms, which use both players' reports to determine whether or not a merger will take place and what each player will earn in each case. When the outside option of at least one player is known, the efficient merger decision can be implemented by such a mechanism under plausible budget-balance requirements. When neither outside option is known, we show that the potential for regret-free implementation is much more limited, unless the budget balance condition is relaxed to permit money-burning in the case of false reports.     

Abstract types and distributions in independent private value auctions

A large body of the mechanism design literature relies on convexity assumptions on the set of types (that is, on the domain of the mechanism). In this note I show that, at least for auction mechanisms with independent signals, it is always possible to extend incentive compatible mechanisms to incentive compatible mechanisms defined on any larger set of types. I acknowledge the comments of Luis Braido, Sérgio Orioli, Humberto Moreira, Frank Page and an anonymous referee. The financial support of Edital Universal 02/06, CNPq is gratefully acknowledged.