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Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff

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  • R. Laraki
  • A. Maitra
  • W. Sudderth

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. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • R. Laraki & A. Maitra & W. Sudderth, 2013. "Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff," Dynamic Games and Applications, Springer, vol. 3(2), pages 162-171, June.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:162-171
    DOI: 10.1007/s13235-012-0054-7
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    References listed on IDEAS

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    1. Ashok P. Maitra & William D. Sudderth, 2007. "Subgame-Perfect Equilibria for Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 711-722, August.
    2. A. Maitra & W. Sudderth, 2003. "Borel stay-in-a-set games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 97-108, December.
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    Cited by:

    1. J'anos Flesch & Arkadi Predtetchinski & Ville Suomala, 2021. "Random perfect information games," Papers 2104.10528, arXiv.org.
    2. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    3. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    4. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2021. "Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels," Dynamic Games and Applications, Springer, vol. 11(4), pages 704-737, December.
    5. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.

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