Existence of Optimal Strategies in Zero-Sum Nonstationary Stochastic Games with Lack of Information on Both Sides

Abstract

This paper studies a zero-sum discrete-time stochastic game model with Borel state and action spaces. The law of motion of the system in the model is assumed to be nonstationary. Following M. Schal, at each stage of the game every player is assumed to know the sequence of states occurring up to this stage, but has no explicit information about his opponent’s previous decisions. Under certain semicontinuity and compactness conditions, the existence of a value is proved for such a game and the existence of optimal ($\varepsilon $-optimal) universally measurable strategies for the minimizes (maximizes). This essentially improves a result of Schal on this subject.