CFDP 1848

On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

Author(s): 

Publication Date: February 2012

Pages: 20

Abstract: 

This paper provides a dual characterization of the limit set of perfect public equilibrium payoffs in stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine and Maskin (1994), Kandori and Matsushima (1998) and Hörner, Sugaya, Takahashi and Vieille (2011) obtain. As a second corollary, in the context of repeated games, it follows that this limit set of payoffs is a polytope (a bounded polyhedron) when attention is restricted to equilibria in pure strategies. We provide a two-player game in which this limit set is not a polytope when mixed strategies are considered.

Keywords: 

Stochastic games, Repeated games, Folk theorem

JEL Classification Codes:  C72, C73

Note: 

Published in Games and Economic Behavior (May 2014), 85: 70-83 [DOI]