Mezzetti, Claudio
Renou, Ludovic
Implementation in Mixed Nash Equilibrium
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implementation
Maskin monotonicity
pure and mixed Nash equilibrium
weak set-monotonicity
social choice correspondence
Financial Economics
2009
2009-04-28
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.
Working or Discussion Paper
English