On Stochastic Games with Uncountable State and Action Spaces

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We consider stochastic games with uncountable state space and prove the existence of a Nash equilibrium in Markovian strategies, reached as a limit, in an appropriate sense, of finite horizon Markovian equilibria (the latter exist even with compact metric action spaces). Our approach is based on Glicksberg’s fixed-point theorem, basic measurable selection results and a generalized Fatou Lemma.