ON ZERO SUM STOCHASTIC GAMES WITH GENERAL STATE SPACE. I
Abstract: The present paper treats of discrete-time stationary models 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 ), a full solution of the finite horizon models is given.
To ensure the existence of value in the infinite 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 -optimal)
strategies for both players rely on iterative, finite horizon to infinite horizon methods.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -