RECURSIVE METHODS IN DISCOUNTED STOCHASTIC GAMES: AN ALGORITHM FOR δ → 1 AND A FOLK THEOREM

• 成果类型: Article
• 署名作者: Hoerner, Johannes; Sugaya, Takuo; Takahashi, Satoru; Vieille, Nicolas
• 署名单位: Yale University; Princeton University; Hautes Etudes Commerciales (HEC) Paris
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA9004
• 发表日期: 2011
• 页码: 1277-1318
• 关键词: long-run; DYNAMICS

摘要

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 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.