Open Access
February, 1985 Universally Measurable Strategies in Zero-Sum Stochastic Games
Andrzej S. Nowak
Ann. Probab. 13(1): 269-287 (February, 1985). DOI: 10.1214/aop/1176993080


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.


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Andrzej S. Nowak. "Universally Measurable Strategies in Zero-Sum Stochastic Games." Ann. Probab. 13 (1) 269 - 287, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0592.90106
MathSciNet: MR770642
Digital Object Identifier: 10.1214/aop/1176993080

Primary: 90D15
Secondary: 28A05 , 60K99 , 93C55

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

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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