The Annals of Probability

Universally Measurable Strategies in Zero-Sum Stochastic Games

Andrzej S. Nowak

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993080

Digital Object Identifier
doi:10.1214/aop/1176993080

Mathematical Reviews number (MathSciNet)
MR770642

Zentralblatt MATH identifier
0592.90106

JSTOR
links.jstor.org

Subjects
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

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

Citation

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


Export citation