The Annals of Probability

Universally Measurable Strategies in Zero-Sum Stochastic Games

Andrzej S. Nowak

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This paper deals with zero-sum discrete-time stationary models of stochastic games with Borel state and action spaces. A mathematical framework introduced here for such games refers to the minimax theorem of Ky Fan involving certain asymmetric assumptions on the primitive data. This approach ensures the existence and the universal measurability of the value functions and the existence for either or both players of optimal or $\varepsilon$-optimal universally measurable strategies in the finite horizon games as well as in certain infinite horizon games. The fundamental result of this paper is a minimax selection theorem extending a selection theorem of Brown and Purves. As applications of this basic result, we obtain some new theorems on absorbing, discounted, and positive stochastic games.

Article information

Ann. Probab., Volume 13, Number 1 (1985), 269-287.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 90D15
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 60K99: None of the above, but in this section 93C55: Discrete-time systems

Zero-sum discrete-time stochastic games optimal stationary strategies universally measurable strategies minimax selection theorem


Nowak, Andrzej S. Universally Measurable Strategies in Zero-Sum Stochastic Games. Ann. Probab. 13 (1985), no. 1, 269--287. doi:10.1214/aop/1176993080.

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