Recursive Methods in Discounted Stochastic Games: An Algorithm for δ → 1 and a Folk Theorem

46 Pages Posted: 22 Dec 2010

See all articles by Johannes Horner

Johannes Horner

Yale University - Cowles Foundation

Takuo Sugaya

Stanford Graduate School of Business

Satoru Takahashi

National University of Singapore (NUS) - Department of Economics

Nicolas Vieille

HEC Paris - Economics & Decision Sciences

Date Written: August 20, 2010

Abstract

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players’) equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.

Keywords: Stochastic Games

JEL Classification: C72, C73

Suggested Citation

Horner, Johannes and Sugaya, Takuo and Takahashi, Satoru and Vieille, Nicolas, Recursive Methods in Discounted Stochastic Games: An Algorithm for δ → 1 and a Folk Theorem (August 20, 2010). Economic Theory Center Working Paper No. 005-2010, Available at SSRN: https://ssrn.com/abstract=1729299 or http://dx.doi.org/10.2139/ssrn.1729299

Johannes Horner (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Takuo Sugaya

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
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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