On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games
22 Pages Posted: 16 Feb 2012
Date Written: February 15, 2012
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: C72, C73
Suggested Citation: Suggested Citation