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Proceedings of the American Mathematical Society

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Approximation theorems for zero-sum nonstationary stochastic games


Author: Andrzej S. Nowak
Journal: Proc. Amer. Math. Soc. 92 (1984), 418-424
MSC: Primary 90D15; Secondary 93E05
DOI: https://doi.org/10.1090/S0002-9939-1984-0759667-1
MathSciNet review: 759667
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Abstract: This paper deals with zero-sum nonstationary stochastic games with countable state and action spaces which include both Shapley's stochastic games [11] and infinite games with imperfect information studied by Orkin in [7]. It is shown that any nonstationary stochastic game with a bounded below lower semicontinuous payoff defined on the space of all histories has a value function and the minimizer has an optimal strategy. Moreover, two approximation theorems extending the main results of Orkin from [7] are established. Finally, counterexamples answering in the negative some open questions raised by Orkin [7] and Sengupta [10] are given.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0759667-1
Keywords: Zero-sum discrete-time nonstationary stochastic game, infinite game, imperfect information
Article copyright: © Copyright 1984 American Mathematical Society