Ergodicity Condition for Zero-Sum Games
Résumé
For zero-sum repeated stochastic games, basic questions are whether the mean payoff per time unit is independent of the initial state, and whether this property is robust to perturbations of rewards. In the case of finite action spaces, we show that the answer to both questions is positive if and only if an ergodicity condition involving fixed points of the recession function of the Shapley operator or reachability in directed hypergraphs is satisfied.