Sensitive equilibria for ergodic stochastic games with countable state spaces |
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Authors: | Andrzej S. Nowak |
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Affiliation: | (1) Radar Division, Naval Research Laboratory, Code 5341, Washington, DC 20375, USA;(2) Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794-3600, USA |
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Abstract: | We consider stochastic games with countable state spaces and unbounded immediate payoff functions. Our assumptions on the transition structure of the game are based on a recent work by Meyn and Tweedie [19] on computable bounds for geometric convergence rates of Markov chains. The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games. By sensitive optimality we mean overtaking or 1-optimality. We also provide a new Nash equilibrium theorem for a class of ergodic nonzero-sum stochastic games with denumerable state spaces. |
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