Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem

47 Pages Posted: 26 Dec 2009 Last revised: 6 Oct 2013

See all articles by Johannes Horner

Johannes Horner

Yale University - Cowles Foundation

Takuo Sugaya

Stanford Graduate School of Business

Satoru Takahashi

Harvard University - Department of Economics

Nicolas Vieille

HEC Paris - Economics & Decision Sciences

Date Written: August 12, 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 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 delta Approaching 1 and a Folk Theorem (August 12, 2010). Cowles Foundation Discussion Paper No. 1742, Available at SSRN: https://ssrn.com/abstract=1526604 or http://dx.doi.org/10.2139/ssrn.1526604

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

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States

Nicolas Vieille

HEC Paris - Economics & Decision Sciences ( email )

Paris
France

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