Abstract
Consider a two-person, zero-sum stochastic game with Borel state space S, finite action sets A,B, and Borel measurable law of motion q. Suppose the payoff is a bounded function f of the infinite history of states and actions that is measurable for the product of the Borel σ-field for S and the σ-fields of all subsets for A and B, and is lower semicontinuous for the product of the discrete topologies on the coordinate spaces. Then the game has a value and player II has a subgame perfect optimal strategy.
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We are grateful for the helpful comments of Andrzej Nowak and two anonymous referees.
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Dedicated to the memory of Ashok Maitra.
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Laraki, R., Maitra, A.P. & Sudderth, W.D. Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff. Dyn Games Appl 3, 162–171 (2013). https://doi.org/10.1007/s13235-012-0054-7
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DOI: https://doi.org/10.1007/s13235-012-0054-7