Mechanism design with side payments: Individual rationality and iterative dominance

In this paper, we investigate the collective decision problem with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. Additionally, with regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.

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

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

[3]  R. McAfee.  Efficient allocation with continuous quantities , 1991 .

[4]  Ky Pan.  5. On Systems of Linear Inequalities , 1957 .

[5]  Hitoshi Matsushima,et al.  Virtual implementation in iteratively undominated strategies: complete information , 1992 .

[6]  Roberto Serrano,et al.  Type Diversity and Virtual Bayesian Implementation , 2001 .

[7]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[8]  Hitoshi Matsushima.  Dominant strategy mechanisms with mutually payoff-relevant private information and with public information , 1990 .

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

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

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

[12]  Anil Arya,et al.  Virtual Implementation in Separable Bayesian Environments Using Simple Mechanisms , 1995 .

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

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

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

[16]  R. Serrano,et al.  Some limitations of virtual Bayesian implementation , 2001 .

[17]  A. S. Solodovnikov,et al.  Systems of Linear Inequalities , 1979 .

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

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

[20]  Jacques Cr.  Balanced Bayesian Mechanisms , 2003 .

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

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

[23]  Hitoshi Matsushima,et al.  Non-Consequential Moral Preferences, Detail-Free Implementation, and Representative Systems ( Revised as CARF-F-062(2006) ) , 2004 .

[24]  R. Rob.  Pollution claim settlements under private information , 1989 .

[25]  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 .

[26]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

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

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

[29]  John Duggan.  Virtual Bayesian Implementation , 1997 .

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