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Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games

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  • Ziliotto, Bruno

Abstract

This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions under which the existence of the asymptotic value implies the convergence of the values of the weighted game, as players get more and more patient. The second application concerns stochastic games with finite state space and action sets. This paper builds a simple class of asymptotically optimal strategies in the weighted game, that at each stage play optimally in a discounted game with a discount factor corresponding to the relative weight of the current stage.

Suggested Citation

  • Ziliotto, Bruno, 2018. "Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 486-503.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:486-503
    DOI: 10.1016/j.geb.2018.01.009
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    References listed on IDEAS

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    1. 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.
    2. Ehud Lehrer & Sylvain Sorin, 1992. "A Uniform Tauberian Theorem in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 303-307, May.
    3. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Post-Print hal-01302553, HAL.
    5. Guillaume Vigeral, 2013. "A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value," Dynamic Games and Applications, Springer, vol. 3(2), pages 172-186, June.
    6. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    7. Bruno Ziliotto, 2016. "General limit value in zero-sum stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 353-374, March.
    8. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302553, HAL.
    9. repec:dau:papers:123456789/10880 is not listed on IDEAS
    10. 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.
    11. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: Uniform value, Tauberian theorem and the Mertens conjecture " M axmin = lim v n = lim v λ "," PSE-Ecole d'économie de Paris (Postprint) hal-01302553, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Tauberian theorem; Nonexpansive operators; Stochastic games; Asymptotic value; Weighted payoffs;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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