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An Application of Ramsey Theorem to stopping Games

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  • VIEILLE, Nicolas
  • SHMAYA, Eran

    ()
    (The School of Mathematical Sciences, Tel Aviv University)

  • SOLAN, Eilon

    ()
    (Kellog Graduate School of Management, Northwestern University)

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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File URL: http://www.hec.fr/var/fre/storage/original/application/652b2e846c7cf2c3164a39901794652f.pdf
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Bibliographic Info

Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 746.

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Length: 13 pages
Date of creation: 24 Jul 2001
Date of revision:
Handle: RePEc:ebg:heccah:0746

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Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
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Keywords: non zero-sum stopping games; Ramsey theorem; equilibrium payoff;

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References

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  1. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer, vol. 18(3), pages 293-310.
  2. Solan, Eilon & Vieille, Nicolas, 2001. "Quitting Games," Economics Papers from University Paris Dauphine 123456789/6017, Paris Dauphine University.
  3. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
  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. 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.
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Citations

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Cited by:
  1. VIEILLE, Nicolas & SOLAN, Eilon, 2001. "Stopping games: recent results," Les Cahiers de Recherche 744, HEC Paris.
  2. 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.
  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. 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).

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