Optimal strategies in a class of zero-sum ergodic stochastic games

In this paper we study zero-sum stochastic games with Borel state spaces. We make some stochastic stability assumptions on the transition structure of the game which imply the so-called w-uniform geometric ergodicity of Markov chains induced by stationary strategies of the players. Under such assumptions and some regularity conditions on the primitive data, we prove the existence of optimal stationary strategies for the players in the expected average payoff stochastic games. We also provide a first result on overtaking optimality in zero-sum stochastic games.