On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

22 Pages Posted: 16 Feb 2012

See all articles by Johannes Horner

Johannes Horner

Yale University - Cowles Foundation

Satoru Takahashi

National University of Singapore (NUS) - Department of Economics

Nicolas Vieille

HEC Paris - Economics & Decision Sciences

Date Written: February 15, 2012

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: C72, C73

Suggested Citation

Horner, Johannes and Takahashi, Satoru and Vieille, Nicolas, On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games (February 15, 2012). Cowles Foundation Discussion Paper No. 1848, Economic Theory Center Working Paper No. 37-2012, Available at SSRN: https://ssrn.com/abstract=2005713 or http://dx.doi.org/10.2139/ssrn.2005713

Johannes Horner (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Satoru Takahashi

National University of Singapore (NUS) - Department of Economics ( email )

1 Arts Link, AS2 #06-02
Singapore 117570, Singapore 119077
Singapore

Nicolas Vieille

HEC Paris - Economics & Decision Sciences ( email )

Paris
France

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