Correlation, independence, and Bayesian incentives

Our goal is to describe the state of the art on Bayesian mechanisms when utility is transferable and only balanced transfers are admissible. New results will be proved along the way, but they will be integrated to the overall picture. We first study a condition on the information structure of the agents (condition B) which is necessary and sufficient to guarantee implementation of any decision rule. We prove constructively that condition B holds generically. We further analyze another condition (condition C), sufficient to guarantee implementation of any efficient decision rule and provide a simple interpretation. Also, we build a counterexample showing that condition C is not necessary to guarantee implementation of any efficient decision rule and then provide a necessary and sufficient condition. A counterexample is constructed to show that there does not always exist efficient Bayesian mechanisms, with three agents. Finally, we exhibit conditions on the information structures that guarantee unique implementation, and show that they hold generically.

[1]  J. Tirole.  Hierarchies and Bureaucracies: On the Role of Collusion in Organizations , 1986 .

[2]  P. Reny,et al.  Correlated Information and Mechanism Design , 1992 .

[3]  R. Myerson,et al.  Efficient and Durable Decision Rules with Incomplete Information , 1983 .

[4]  David E. M. Sappington,et al.  Licensing and the sharing of knowledge in research joint ventures , 1992 .

[5]  Kalyan Chatterjee,et al.  Bargaining under Incomplete Information , 1983, Oper. Res..

[6]  Jerry R. Green,et al.  Incentives in public decision-making , 1979 .

[7]  Claudio Mezzetti,et al.  Bayesian and Weakly Robust First Best Mechanisms: Characterizations , 1994 .

[8]  Louis-André Gérard-Varet,et al.  Non-Transferable Utility and Bayesian Incentives , 1992 .

[9]  Jacques Cr.  Incentives and the Existence of Pareto-Optimal Revelation Mechanisms , 1990 .

[10]  Richard P. McLean,et al.  FULL EXTRACTION OF THE SURPLUS IN BAYESIAN AND DOMINANT STRATEGY AUCTIONS , 1988 .

[11]  P. Cramton,et al.  Dissolving a Partnership Efficiently , 1985 .

[12]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[13]  R. Myerson.  Incentive Compatibility and the Bargaining Problem , 1979 .

[14]  Dilip Mookherjee,et al.  Implementation via Augmented Revelation Mechanisms , 1990 .

[15]  T. Palfrey.  Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design , 1990 .

[16]  Karlene H. Roberts.  Cartel Behaviour and Adverse Selection , 1985 .

[17]  E. Maskin,et al.  The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility , 1979 .

[18]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[19]  Françoise Forges,et al.  The ex ante incentive compatible core in the absence of wealth effects , 2002 .

[20]  R. Zeckhauser,et al.  Efficiency Despite Mutually Payoff-Relevant Private Information: The Finite Case , 1990 .

[21]  E. Maskin.  Nash Equilibrium and Welfare Optimality , 1999 .

[22]  Steven R. Williams,et al.  Bilateral trade with the sealed bid k-double auction: Existence and efficiency , 1989 .

[23]  Robert H. Wilson.  Incentive Efficiency of Double Auctions , 1985 .

[24]  Stefan Reichelstein,et al.  On the Informational Requirements for the Implementation of Social Choice Rules , 1981 .

[25]  Jacques Crémer,et al.  Balanced Bayesian Mechanisms ∗ , 2017 .

[26]  R. McAfee,et al.  Auctions and Bidding , 1986 .

[27]  Paul R. Milgrom,et al.  The value of information in a sealed-bid auction , 1982 .

[28]  Jacques Crémer,et al.  Incentives and the existence of Pareto-optimal revelation , 1990 .

[29]  Michael H. Riordan,et al.  Uncertainty, Asymmetric Information and Bilateral Contracts , 1984 .

[30]  Theodore Groves,et al.  The Existence of Efficient and Incentive Compatible Equilibria with Public Goods , 1980 .

[31]  Jacques Crémer,et al.  Unique Implementation in Auctions and in Public Goods Problems , 1997 .

[32]  L. Hurwicz,et al.  Social Goals and Social Organization , 1986 .

[33]  Claude d'Aspremont,et al.  On the existence of Bayesian and non-Bayesian revelation of mechanisms , 1987 .

[34]  Hitoshi Matsushima,et al.  Incentive compatible mechanisms with full transferability , 1991 .

[35]  Michael J. Boskin,et al.  Economics and human welfare : essays in honor of Tibor Scitovsky , 1979 .

[36]  Louis-André Gérard-Varet,et al.  Incentive game with incomplete information: an application to a public input model , 1975 .

[37]  D. Fudenberg,et al.  Digitized by the Internet Archive in 2011 with Funding from Working Paper Department of Economics the Folk Theorem with Imperfect Public Information , 2022 .

[38]  John. Moore,et al.  Stopping agents from “cheating” , 1988 .

[39]  Jacques Cremer,et al.  On Governing Multilateral Transactions with Bilateral Contracts , 1987 .

[40]  Drew Fudenberg,et al.  Balanced-Budget Mechanisms with Incomplete Information , 1996 .

[41]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[42]  Hitoshi Matsushima.  Bayesian Monotonicity with Side Payments , 1993 .

[43]  Andrew Postlewaite,et al.  Implementation in differential information economies , 1986 .

[44]  Jacques Cremer,et al.  A Sequential Solution to the Public Goods Problem , 1985 .

[45]  Masaki Aoyagi,et al.  Correlated Types and Bayesian Incentive Compatible Mechanisms with Budget Balance , 1998 .

[46]  E. Maskin.  The Theory of Implementation in Nash Equilibrium: A Survey , 1983 .

[47]  Peter Cramton,et al.  Cartel Enforcement with Uncertainty About Costs , 1990 .

[48]  Richard P. McLean,et al.  Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent , 1985 .

[49]  Françoise Forges,et al.  The ex ante incentive compatible core of the assignment game , 2004, Math. Soc. Sci..

[50]  M. Walker.  On the Nonexistence of a Dominant Strategy Mechanism for Making Optimal Public Decisions , 1980 .

[51]  L. J. Savage.  Elicitation of Personal Probabilities and Expectations , 1971 .

[52]  Georgia Kosmopoulou.  Efficient Bayesian Mechanisms for Collective Goods: Is a Deficit Inevitable? , 2001 .

[53]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[54]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[55]  C. d'Aspremont,et al.  Incentives and incomplete information , 1979 .

[56]  Claude d'Aspremont,et al.  Bayesian incentive compatible beliefs , 1982 .

[57]  Claude d'Aspremont,et al.  Knowledge as a public good: efficient sharing and incentives for development effort , 1998 .

[58]  David Gale.  The theory of linear economic models , 1960 .

[59]  Kim-Sau Chung,et al.  A Note on Matsushima's Regularity Condition , 1999 .

[60]  Jacques Crémer.  Manipulations by Coalitions Under Asymmetric Information: The Case of Groves Mechanisms , 1996 .

[61]  Sanjay Srivastava,et al.  Efficient Trading Mechanisms with Pre-Play Communication , 1991 .

[62]  Roy Radner,et al.  Equilibria of the Sealed- Bid Mechanism for Bargaining with Incomplete Information*, ' , 1987 .

[63]  Eric Maskin,et al.  A Differential Approach to Expected Utility Maximizing Mechanisms , 1979 .

[64]  K. Arrow.  The Property Rights Doctrine and Demand Revelation under Incomplete Information**This work was supported by National Science Foundation under Grant No. SOC75-21820 at the Institute for Mathematical Studies in the Social Sciences, Stanford University. , 1979 .

[65]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[66]  Robert M. Townsend,et al.  Resource Allocation under Asymmetric Information , 1981 .