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We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].
Bellman systems corresponding to stochastic differential games arising from a cost functional which models risk aspects are considered. Here it leads to diagonal elliptic systems without zero order term so that no simple -estimate is available.
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