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Stochastic games with short-stage duration

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  • Abraham Neyman

Abstract

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t 0}$ as the stage duration $\delta$ goes to $0$, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.

Suggested Citation

  • Abraham Neyman, 2013. "Stochastic games with short-stage duration," Discussion Paper Series dp636, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp636
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    References listed on IDEAS

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    1. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    2. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    3. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    4. Eilon Solan & Rakesh V. Vohra, 2002. "Correlated equilibrium payoffs and public signalling in absorbing games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 91-121.
    5. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
    6. repec:dau:papers:123456789/6019 is not listed on IDEAS
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Sylvain Sorin, 2018. "Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 51-63, February.
    3. Sylvain Sorin & Guillaume Vigeral, 2016. "Operator approach to values of stochastic games with varying stage duration," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 389-410, March.
    4. Jan-Henrik Steg, 2018. "On Preemption in Discrete and Continuous Time," Dynamic Games and Applications, Springer, vol. 8(4), pages 918-938, December.
    5. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    6. Fabien Gensbittel & Catherine Rainer, 2018. "A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion," Dynamic Games and Applications, Springer, vol. 8(2), pages 280-314, June.

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