On stochastic games with additive reward and transition structure
type: Item
instance of: scholarly article
title: On stochastic games with additive reward and transition structure
zbMATH Open document ID: 0556.90101
DOI: 10.1007/BF00942191
author: Stef Tijs
author: K. Vrieze
author: Thirukkannamangai E. S. Raghavan
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: We introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player. For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 91A60
zbMATH DE Number: 3887479
zbMATH Keywords: discounted payoff
zbMATH Keywords: two-person stochastic games
zbMATH Keywords: orderfield property
zbMATH Keywords: infinite-horizon
zbMATH Keywords: optimal pure stationary strategies
zbMATH Keywords: undiscounted payoff criterion
zbMATH Keywords: algorithms
zbMATH Keywords: stationary equilibrium
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3887479