In this paper we focus on stochastic games with nitely many states and actions. For this setting we study the epistemic concept of common belief in future rationality, which is based on the condition that players always believe that their opponents will choose rationally in the future. We distinguish two di⁄erent versions of the concept one for the discounted case with a xed discount factor ; and one for the case of uniform optimality, where optimality is required for all discount factors close enough to 1. We show that both versions of common belief in future rationality are always possible in every stochastic game, and always allow for stationary optimal strategies. That is, for both versions we can always nd belief hierarchies that express common belief in future rationality, and that have stationary optimal strategies. We also provide an epistemic characterization of subgame perfect equilibrium for two-player stochastic games, showing that it is equivalent to mutual belief in future rationality together with some correct beliefs assumption.
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- epistemic game theory, stochastic games, common belief in future rationality, Common belief in future rationality, PERFECT-INFORMATION, Stochastic games, BAYESIAN PLAYERS, Epistemic game theory, EQUILIBRIUM, INDUCTION, BELIEF