Markov Games under a Geometric Drift Condition

Zero-sum stochastic games with the expected average cost criterion and unbounded stage cost are studied. It is assumed that the transition probabilities of the Markov chains induced by stationary strategies satisfy a certain geometric drift condition. Under additional assumptions concerning especially the existence of e-optimal strategies in corresponding one-stage games it is shown that the average optimality equation has a solution and that both players have e-optimal stationary strategies.