Skip to main content
Article thumbnail
Location of Repository

Implementation in mixed Nash equilibrium

By Claudio Mezzetti and Ludovic Renou


Updated January 2010A 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

Topics: implementation, Maskin monotonicity, pure and mixed Nash equilibrium, weak set-monotonicity, social choice correspondence
Publisher: Dept. of Economics, University of Leicester
Year: 2009
OAI identifier:

Suggested articles


  1. (1998). A New Approach to the Implementation Problem,” doi
  2. (2003). Behavioral Game Theory: Experiments on Strategic Interaction,” Princeton: doi
  3. (1973). Games with Randomly Disturbed Payoffs: A New Rationale for Mixed-Strategy Equilibrium Points,” doi
  4. (1994). Implementation in Undominated Nash Equilibria without doi
  5. (2002). Implementation Theory,” doi
  6. (2009). Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach to Exact and Approximate Implementation,” Working Paper, doi
  7. (1991). On the Necessary and Sufficient Conditions for
  8. (1998). Strategyproof Probabilistic Rules for Expected Utility doi
  9. (2007). Subgame Perfect Implementation of Voting Rules via Randomized Mechanisms,” doi
  10. (1992). Virtual Implementation in Iteratively Undominated Strategies: doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.