Zero-Sum Stochastic Games in Borel Spaces: Average Payoff Criteria

This paper is concerned with two-person zero-sum dynamic stochastic games in Borel spaces, with possibly unbounded payoff function, and several average (or ergodic) payoff criteria. We give conditions under which the long-run expected average payoff criterion, the sample-path average criterion, the existence of solutions to the average payoff Shapley equations, and a certain "martingale condition" are all equivalent.