On Multichain Markov Games

Two-person, zero-sum Markov games with arbitrary (Borel) state and action spaces, unbounded stage costs, and the average cost criterion are considered. The assumption on the transition probabilities implies some n-stage contraction property and lets the Markov chain of the states under a given strategy pair have several periodic recurrence classes, but the recurrence structure of all possible resulting Markov chains is identical. Under this assumption, some results are presented concerning the existence of 8-optimal strategies.