VIRTUAL IMPLEMENTATION IN NASH EQUILIBRIUM

The two-person case needs to be considered separately. We provide a complete characterization of virtually implementable two-person social choice functions. While not all two-person social choice functions are virtually implementable, our necessary and sufficient condition is simple. This contrasts with the rather complex necessary and sufficient conditions for exact implementation. We show how our results can be extended to implementation in strict Nash equilibrium and coalition-proof Nash equilibrium, to social choice correspondences which map from cardinal preference profiles to lotteries, and to environments with a continuum of pure alternatives.

[1]  O. Hart,et al.  Incomplete Contracts and Renegotiation , 1988 .

[2]  Hitoshi Matsushima.  A new approach to the implementation problem , 1988 .

[3]  David Schmeidler,et al.  CONSTRUCTION OF OUTCOME FUNCTIONS GUARANTEEING , 1978 .

[4]  Eitan Muller,et al.  The equivalence of strong positive association and strategy-proofness , 1977 .

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

[6]  Robert J. Aumann,et al.  16. Acceptable Points in General Cooperative n-Person Games , 1959 .

[7]  M. Whinston,et al.  Coalition-Proof Nash Equilibria II. Applications , 1987 .

[8]  Robin Farquharson,et al.  Theory of voting , 1969 .

[9]  H. Moulin.  The strategy of social choice , 1983 .

[10]  Richard J. Zeckhauser,et al.  Majority Rule with Lotteries on Alternatives , 1969 .

[11]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[12]  Arunava Sen,et al.  A Necessary and Sufficient Condition for Two-Person Nash Implementation , 1991 .

[13]  A. Gibbard.  Manipulation of Schemes That Mix Voting with Chance , 1977 .

[14]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[15]  M. Jackson.  Implementation in Undominated Strategies: A Look at Bounded Mechanisms , 1992 .

[16]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[17]  H. Moulin.  Dominance Solvable Voting Schemes , 1979 .

[18]  M. Whinston,et al.  Coalition-Proof Nash Equilibria I. Concepts , 1987 .

[19]  L. Hurwicz.  Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points , 1979 .

[20]  Mark A Walker,et al.  A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations , 1981 .

[21]  Thomas R. Palfrey,et al.  Nash Implementation Using Undominated Strategies , 1991 .

[22]  John. Moore,et al.  Subgame Perfect Implementation , 1988 .

[23]  T. Saijo,et al.  On constant maskin monotonic social choice functions , 1987 .

[24]  Dilip Abreu,et al.  Subgame perfect implementation: A necessary and almost sufficient condition , 1990 .