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Finitely Additive and Measurable Stochastic Games

Author

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  • Maitra, A
  • Sudderth, W

Abstract

We consider two-person zero-sum stochastic games with arbitrary state and action spaces, a finitely additive law of motion and limit superior payoff function. The players use finitely additive strategies and it is shown that such a game has a value, if the payoff function is evaluated in accordance with the theory of strategic measures as developed by Dubins and Savage. Moreover, when a Borel Structure is imposed on the problem, together with an equicontinuity condition on the law of motion, the value of the game is the same whether calculated in terms of countably additive strategies or finitely additive one.

Suggested Citation

  • Maitra, A & Sudderth, W, 1993. "Finitely Additive and Measurable Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 201-223.
    • Handle: RePEc:spr:jogath:v:22:y:1993:i:3:p:201-23
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Flesch, Janos & Vermeulen, Dries & Zseleva, Anna, 2018. "Existence of justifiable equilibrium," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. J. Flesch & J. Kuipers & G. Schoenmakers & K. Vrieze, 2010. "Subgame Perfection in Positive Recursive Games with Perfect Information," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 193-207, February.
    6. Barelli, Paulo & Duggan, John, 2014. "A note on semi-Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 151(C), pages 596-604.
    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. William D. Sudderth, 2016. "Finitely Additive Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 92-108, February.
    9. Flesch, János & Vermeulen, Dries & Zseleva, Anna, 2017. "Zero-sum games with charges," Games and Economic Behavior, Elsevier, vol. 102(C), pages 666-686.
    10. János Flesch & Arkadi Predtetchinski & William Sudderth, 2021. "Discrete stop-or-go games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 559-579, June.

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