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An Application of Ramsey Theorem to Stopping Games

Author

Listed:
  • Eran Shmaya
  • Eilon Solan
  • Nicolas Vieille

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.
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Suggested Citation

  • Eran Shmaya & Eilon Solan & Nicolas Vieille, 2001. "An Application of Ramsey Theorem to Stopping Games," Discussion Papers 1323, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1323
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1323.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. repec:dau:papers:123456789/6017 is not listed on IDEAS
    3. 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.
    4. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Eilon Solan & Nicolas Vieille, 2001. "Stopping Games: recent results," Working Papers hal-00595484, HAL.
    2. Flesch János & Kuipers Jeroen & Schoenmakers Gijs & Vrieze Koos, 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).
    3. 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.
    4. 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.
    5. 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.

    More about this item

    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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