The optimality equation and ϵ-optimal strategies in Markov games with average reward criterion

In this paper we consider two-person zero-sum stochastic games with unbounded payoffs and the average reward criterion. State and action spaces are assumed to be Borel spaces. Under conditions which are more general than the ergodicity assumptions in related works, we show that the optimality equation has a solution and that ϵ-optimal stationary strategies exist. Our proofs use a completely different approach compared to the above mentioned papers. We prove that operators of a parameterized class have fixed points, and then we use continuity and monotonicity properties of these fixed points with respect to the class parameter to show that the optimality equation has a solution.