Implementation in Mixed Nash Equilibrium

Claudio Mezzetti and Ludovic Renou

No 09/10, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

Abstract: A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibrium outcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of Nash implementation in that it does not require each optimal alternative to be the outcome of a pure Nash equilibrium. We show that the condition of weak set-monotonicity, a weakening of Maskin’s monotonicity, is necessary for implementation. We provide sufficient conditions for implementation and show that important social choice correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

Keywords: implementation; Maskin monotonicity; pure and mixed Nash equilibrium; weak set-monotonicity; social choice correspondence (search for similar items in EconPapers)
JEL-codes: C72 D71 (search for similar items in EconPapers)
Date: 2009-04, Revised 2010-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Implementation in mixed Nash equilibrium (2012)
Working Paper: Implementation in Mixed Nash Equilibrium (2012)
Working Paper: Implementation in Mixed Nash Equilibrium (2009)
Working Paper: Implementation in Mixed Nash Equilibrium (2009)
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