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Implementation in mixed Nash equilibrium

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  • Mezzetti, Claudio
  • Renou, Ludovic

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 for all cardinal representations of the preference profile. Unlike Maskinʼs definition, our definition does not require each optimal alternative to be the outcome of a pure equilibrium. We show that set-monotonicity, a weakening of Maskinʼs monotonicity, is necessary for mixed Nash implementation. With at least three players, set-monotonicity and no-veto power are sufficient. Important correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 6 ()
Pages: 2357-2375

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:6:p:2357-2375

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Implementation; Maskin monotonicity; Pure and mixed Nash equilibrium; Set-monotonicity; Social choice correspondence;

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References

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Cited by:
  1. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
  2. Dirk Bergemann & Stephen Morris, 2009. "Rationalizable Implementation," Cowles Foundation Discussion Papers 1697, Cowles Foundation for Research in Economics, Yale University.
  3. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.

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