Stochastic games without perfect monitoring

A two-person zero-sum stochastic game with finitely many states and actions is considered. The classical assumption of perfect monitoring is relaxed. Instead of being informed of the previous action of his opponent, each player receives a random signal, the law of which depending on both previous actions and on the previous state. We prove the existence of the max–min and dually of the min–max, thus extending both the result of Mertens–Neyman about the existence of the value in case of perfect monitoring and a theorem obtained by the author on a subclass of stochastic games: the absorbing games.