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Finitely additive stochastic games with Borel measurable payoffs

Author

Listed:
  • A. Maitra

    (University of Minnesota, School of Statistics, 270 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455-8868, USA)

  • W. Sudderth

    (University of Minnesota, School of Statistics, 270 Vincent Hall, 206 Church Street S.E., Minneapolis, MN 55455-8868, USA)

Abstract

We prove that a two-person, zero-sum stochastic game with arbitrary state and action spaces, a finitely additive law of motion and a bounded Borel measurable payoff has a value.

Suggested Citation

  • A. Maitra & W. Sudderth, 1998. "Finitely additive stochastic games with Borel measurable payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 257-267.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:2:p:257-267
    Note: Received December 1996/Final version November 1997
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    Citations

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    Cited by:

    1. Shmaya, Eran & Solan, Eilon, 2004. "Zero-sum dynamic games and a stochastic variation of Ramsey's theorem," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 319-329, August.
    2. Hugo Gimbert & Jérôme Renault & Sylvain Sorin & Xavier Venel & Wieslaw Zielonka, 2016. "On the values of repeated games with signals," PSE-Ecole d'économie de Paris (Postprint) hal-01006951, HAL.
    3. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Itai Arieli & Yehuda Levy, 2011. "Infinite sequential games with perfect but incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 207-213, May.
    5. János Flesch & Dries Vermeulen & Anna Zseleva, 2021. "Legitimate equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 787-800, December.
    6. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    7. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
    8. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2008. "Stochastic Games on a Product State Space," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 403-420, May.
    9. Flesch, Janos & Vermeulen, Dries & Zseleva, Anna, 2018. "Existence of justifiable equilibrium," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    10. János Flesch & Dries Vermeulen & Anna Zseleva, 2019. "Catch games: the impact of modeling decisions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 513-541, June.
    11. János Flesch & Dries Vermeulen & Anna Zseleva, 2024. "Finitely additive behavioral strategies: when do they induce an unambiguous expected payoff?," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 695-723, June.
    12. 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.
    13. William D. Sudderth, 2016. "Finitely Additive Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 92-108, February.
    14. Flesch, János & Vermeulen, Dries & Zseleva, Anna, 2017. "Zero-sum games with charges," Games and Economic Behavior, Elsevier, vol. 102(C), pages 666-686.

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