Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space
type: Item
instance of: scholarly article
title: Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space
zbMATH Open document ID: 0543.90101
DOI: 10.1007/BF00939136
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: This paper considers discounted noncooperative stochastic games with uncountable state space and compact metric action spaces. We assume that the transition law is absolutely continuous with respect to some probability measure defined on the state space. We prove, under certain additional continuity and integrability conditions, that such games have \(\epsilon\)-equilibrium stationary strategies for each \(\epsilon>0\). To prove this fact, we provide a method for approximating the original game by a sequence of finite or countable state games. The main result of this paper answers partially a question raised by \textit{T. Parthasarathy} [Sankhya, Ser. A 44, 114-127 (1982)].
Mathematics Subject Classification ID: 91A15
zbMATH DE Number: 3865017
zbMATH Keywords: discounted rewards
zbMATH Keywords: approximation of discounted stochastic games
zbMATH Keywords: epsilon-equilibrium
zbMATH Keywords: discounted noncooperative stochastic games
zbMATH Keywords: uncountable state space
zbMATH Keywords: compact metric action spaces
zbMATH Keywords: equilibrium stationary strategies
author: Andrzej S. Nowak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3865017