Title

On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

Author(s)

Johannes H�rner Johannes H�rner (Yale University)

Satoru Takahashi Satoru Takahashi (Princeton University)

Nicolas Vieille Nicolas Vieille (HEC Paris)

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 Horrner, 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.

Creation Date

2012-02

Section URL ID

ET

Paper Number

wp037_2012_Horner_Takahashi_Vielle_On%20the%20Limit%20Equilibrium.pdf

URL

http://detc.princeton.edu/wp-content/uploads/2016/11/wp037_2012_Horner_Takahashi_Vielle_On-the-Limit-Equilibrium.pdf

File Function

Jel

C72, C73

Keyword(s)

stochastic games, repeated games, folk theorem

Suppress

false

Series

10