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An Application of Ramsey Theorem to Stopping Games

Author

Listed:
  • Eran Shmaya

    (Kellogg [Northwestern] - Kellogg School of Management [Northwestern University, Evanston] - Northwestern University [Evanston], TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Eilon Solan

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We prove that every two-player non zero-sum deterministic stopping game with uniformly bounded payoffs admits an e-equilibrium, for every e > 0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite subgraph which is monochromatic.

Suggested Citation

  • Eran Shmaya & Eilon Solan & Nicolas Vieille, 2001. "An Application of Ramsey Theorem to Stopping Games," Working Papers hal-00595481, HAL.
    • Handle: RePEc:hal:wpaper:hal-00595481
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    References listed on IDEAS

    as
    1. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. repec:dau:papers:123456789/6017 is not listed on IDEAS
    4. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
    5. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
    6. Yoshio Ohtsubo, 1987. "A Nonzero-Sum Extension of Dynkin's Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 277-296, May.
    7. J. Flesch & F. Thuijsman & O. J. Vrieze, 1996. "Recursive Repeated Games with Absorbing States," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1016-1022, November.
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    Cited by:

    1. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2008. "Subgame-perfection in stochastic games with perfect information and recursive payoffs," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Eilon Solan & Nicolas Vieille, 2001. "Stopping Games: recent results," Working Papers hal-00595484, HAL.
    3. Eilon Solan, 2002. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Discussion Papers 1356, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.
    5. Eran Shmaya & Eilon Solan, 2002. "Two Player Non Zero-Sum Stopping Games in Discrete Time," Discussion Papers 1347, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
    7. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    8. 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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    More about this item

    Keywords

    Non zero-sum stopping games; Ramsey Theorem; equilibrium payoff;
    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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