Semicontinuous nonstationary stochastic games. II
type: Item
instance of: scholarly article
title: Semicontinuous nonstationary stochastic games. II
zbMATH Open document ID: 0712.90101
DOI: 10.1016/0022-247X(90)90025-B
author: Andrzej S. Nowak
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: This paper is a continuation of an earlier work of the author [ibid. 117, 84-99 (1986; Zbl 0594.90105)], which was devoted to general stochastic dynamic games with zero-sum, metric state spaces, weakly continuous transition probabilities, and lower semi-continuous payoff function. In this paper transition probabilities are assumed to be norm continuous, but with respect to actions of one player only (the minimizer). The payoff function depends lower semicontinuously on the minimizer's actions and is measurable with respect to random states of the game. Some general conditions that guarantee the existence of a value and optimal strategies for the players are given. It is also shown that the minimizer (whose action spaces are assumed to be compact) has a subgame-perfect optimal strategy. We point out that zero-sum Markov games belong to the large class of stochastic games studied in this paper.
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 4172792
zbMATH Keywords: norm continuous transition probabilities
zbMATH Keywords: lower semi-continuous payoff function
zbMATH Keywords: existence of a value
zbMATH Keywords: optimal strategies
zbMATH Keywords: subgame-perfect optimal strategy
zbMATH Keywords: zero-sum Markov games
MaRDI profile type: Publication
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full work available at URL: 0022-247x(90)90025-b
OpenAlex ID: W4205875884
description: scientific article; zbMATH DE number 4172792