Recursive Methods in Discounted Stochastic Games: An Algorithm for Delta Approaching 1 and a Folk Theorem
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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.
Hörner, Johannes; Sugaya, Takuo; Takahashi, Satoru; and Vieille, Nicolas, "Recursive Methods in Discounted Stochastic Games: An Algorithm for Delta Approaching 1 and a Folk Theorem" (2009). Cowles Foundation Discussion Papers. 2066.