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Stopping games and Ramsey theorem

Author

Listed:
  • Eran Schmaya

    (TAU - Tel Aviv University)

  • Eilon Solan

    (Northwestern University [Evanston])

  • Nicolas Vieille

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - 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 epsilon-equilibrium, for every epsilon>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 Schmaya & Eilon Solan & Nicolas Vieille, 2002. "Stopping games and Ramsey theorem," Working Papers hal-00242997, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242997
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242997v1
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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. 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.
    3. Yoshio Ohtsubo, 1987. "A Nonzero-Sum Extension of Dynkin's Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 277-296, May.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.

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