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In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated ergodic optimality equations admit unique solutions. Finally, the existence of Nash-equilibrium in randomized stationary strategies is established by showing that an appropriate set-valued map has a fixed point.
Bose et al. (Fri,) studied this question.