Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff

Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f is measurable for the product of the Borel sigma-fields of the coordinate spaces and is lower semi continuous for the product of the discrete topologies on the coordinate spaces. Then the game has a value and player II has a subgame perfect optimal strategy. Mots clés : Jeux stochastiques, perfection en sous jeux, ensembles Boréliens.