On zero-sum stochastic games with general state space

Abstract: The present paper treats of discrete-time stationary model s of stochastic games with an abstract measurable state space and separable metric action spaces. Under different assumptions on the state space, action spaces , the reward function, and the law of motion (assumptions (M1), (M2), (M3)), a full solution of the finite horizon models is given. To ensure the existence of value in the in finite horizon models we impose some convergence conditions (conditions (D) and ( P)) on the expected rewards, thus including the discounted case. The proofs of the existence of optimal (or ε-optimal) strategies for both players rely on iterative, fin ite horizon to infinite horizon methods.