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Weighted-average stochastic games with constant payoff

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  • Miquel Oliu-Barton

    (Université Paris-Dauphine)

Abstract

In a zero-sum stochastic game, at each stage, two opponents make decisions which determine a stage reward and the law of the state of nature at the next stage, and the aim of the players is to maximize the weighted-average of the stage rewards. In this paper we solve the constant-payoff conjecture formulated by Sorin, Venel and Vigeral in 2010 for two classes of stochastic games with weighted-average rewards: (1) absorbing games, a well-known class of stochastic games where the state changes at most once during the game, and (2) smooth stochastic games, a newly introduced class of stochastic games where the state evolves smoothly under optimal play.

Suggested Citation

  • Miquel Oliu-Barton, 2022. "Weighted-average stochastic games with constant payoff," Operational Research, Springer, vol. 22(3), pages 1675-1696, July.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:3:d:10.1007_s12351-021-00625-6
    DOI: 10.1007/s12351-021-00625-6
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    References listed on IDEAS

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    1. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    2. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    3. Luc Attia & Miquel Oliu-Barton, 2019. "A formula for the value of a stochastic game," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(52), pages 26435-26443, December.
    4. Bruno Ziliotto, 2016. "A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1522-1534, November.
    5. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    6. Sylvain Sorin & Guillaume Vigeral, 2020. "Limit Optimal Trajectories in Zero-Sum Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 555-572, June.
    7. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
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