Stochastic games on a product state space: the periodic case |
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Authors: | János Flesch Gijs Schoenmakers Koos Vrieze |
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Affiliation: | (1) Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands;(2) Department of Mathematics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands |
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Abstract: | We examine so-called product-games. These are n-player stochastic games played on a product state space S 1 × ... × S n , in which player i controls the transitions on S i . For the general n-player case, we establish the existence of 0-equilibria. In addition, for the case of two-player zero-sum games of this type, we show that both players have stationary 0-optimal strategies. In the analysis of product-games, interestingly, a central role is played by the periodic features of the transition structure. Flesch et al. (Math Oper Res 33, 403–420, 2008) showed the existence of 0-equilibria under the assumption that, for every player i, the transition structure on S i is aperiodic. In this article, we examine product-games with periodic transition structures. Even though a large part of the approach in Flesch et al. (Math Oper Res 33, 403–420, 2008) remains applicable, we encounter a number of tricky problems that we have to address. We provide illustrative examples to clarify the essence of the difference between the aperiodic and periodic cases. |
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Keywords: | Noncooperative games Stochastic games Periodic Markov decision problems Equilibria |
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