Existence of Value and Randomized Strategies in Zero-Sum Discrete-Time Stochastic Dynamic Games
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Two players with conflicting objectives are simultaneously controlling a discrete-time stochastic system. The goal of this paper is to analyze such zero-sum, discrete-time, stochastic systems, when the two players are allowed to use randomized strategies. Previous results have been restricted to systems with finite or compact state spaces. The present results are proved for complete, separable, metric spaces which are very useful for applications. All previously known results then emerge as special cases. In addition, a variety of conjectures and open problems are resolved regarding the existence of a value function, its properties such as Borel measurability or continuity, and the existence for either or both players of optimal or epsilon -optimal stationary strategies.
