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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The completely mixed single-controller stochastic game

Author: Jerzy A. Filar
Journal: Proc. Amer. Math. Soc. 95 (1985), 585-594
MSC: Primary 90D15
MathSciNet review: 810169
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Abstract: We consider a zero-sum stochastic game with finitely many states and actions. Further we assume that the transition probabilities depend on the actions of only one player (player II, in our case), and that the game is completely mixed. That is, every optimal stationary strategy for either player assigns a positive probability to every action in every state. For these games, properties analogous to those derived by Kaplansky [4] for the completely mixed matrix games, are established in this paper. These properties lead to the counterintuitive conclusion that the controller need not know the law of motion in order to play optimally, but his opponent does not have this luxury.

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Keywords: Stochastic games, single-controller, completely mixed property, stationary strategies
Article copyright: © Copyright 1985 American Mathematical Society