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We deal with discounted ARAT stochastic games on a Borel state space with finite action spaces and nonatomic transition probabilities. We prove the existence of pure Nash equilibria in stationary almost Markov strategies that depend only on the current and previous state of the game. Our proof is based on an existence theorem for correlated equilibria in stochastic games and some results on the integrals of set-valued mappings with respect to a probability measure depending on a parameter.

On pure stationary almost Markov Nash equilibria in nonzero-sum ARAT stochastic games