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.
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Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number
09/10.
Length: Date of creation: Apr 2009 Date of revision: Handle: RePEc:lec:leecon:09/10
Contact details of provider: Postal: Department of Economics University of Leicester, University Road. Leicester. LE1 7RH. UK Phone: +44 (0)116 252 2887 Fax: +44 (0)116 252 2908 Email: Web page: http://www.le.ac.uk/economics/
Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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