Universally measurable strategies in zero-sum stochastic games
type: Item
instance of: scholarly article
title: Universally measurable strategies in zero-sum stochastic games
zbMATH Open document ID: 0592.90106
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: This paper deals with zero-sum discrete-time stationary models of stochastic games with Borel state and action spaces. It is known that the value function of a Borel space stochastic game which satisfies neither semi-continuity nor compactness conditions need not be universally measurable [\textit{U. Rieder}, On semi-continuous dynamic games, Tech. Rep., Univ. Karlsruhe (1978)]. The main purpose of this paper is to give some semi-continuity and compactness conditions that ensure the existence and universal measurability of the value function of the game as well as the existence of universally measurable optimal strategies for both players. The fundamental result in this paper is a minimax selection theorem extending a selection theorem of \textit{L. D. Brown} and \textit{R. Purves} [Ann. Statist. 1, 902-912 (1973; Zbl 0265.28003)]. As applications of this basic result, some new theorems on absorbing discounted, and positive stochastic games are proved.
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 3952538
zbMATH Keywords: optimal stationary strategies
zbMATH Keywords: zero-sum discrete-time stationary models of stochastic games
zbMATH Keywords: Borel state and action spaces
zbMATH Keywords: semi-continuity and compactness conditions
zbMATH Keywords: existence and universal measurability of the value function
zbMATH Keywords: universally measurable optimal strategies
zbMATH Keywords: minimax selection theorem
zbMATH Keywords: absorbing discounted, and positive stochastic games
author: Andrzej S. Nowak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993080
OpenAlex ID: W2030913362
DOI: 10.1214/AOP/1176993080
description: scientific article; zbMATH DE number 3952538