IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00595481.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    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.
    6. 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.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eran Schmaya & Eilon Solan & Nicolas Vieille, 2002. "Stopping games and Ramsey theorem," Working Papers hal-00242997, HAL.
    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.
    3. VIEILLE, Nicolas & SOLAN, Eilon, 2001. "Stopping games: recent results," HEC Research Papers Series 744, HEC Paris.
    4. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    5. Eilon Solan & Nicolas Vieille, 2001. "Quitting Games," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 265-285, May.
    6. 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.
    7. Flesch, J. & Thuijsman, F. & Vrieze, O.J., 2007. "Stochastic games with additive transitions," European Journal of Operational Research, Elsevier, vol. 179(2), pages 483-497, June.
    8. Sandroni, Alvaro & Urgun, Can, 2017. "Dynamics in Art of War," Mathematical Social Sciences, Elsevier, vol. 86(C), pages 51-58.
    9. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    10. Yu-Jui Huang & Zhou Zhou, 2022. "A time-inconsistent Dynkin game: from intra-personal to inter-personal equilibria," Finance and Stochastics, Springer, vol. 26(2), pages 301-334, April.
    11. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.
    12. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.
    13. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    14. Yu-Jui Huang & Zhou Zhou, 2021. "A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria," Papers 2101.00343, arXiv.org, revised Dec 2021.
    15. Elżbieta Ferenstein, 2007. "Randomized stopping games and Markov market games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 531-544, December.
    16. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.
    17. Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    18. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
    19. Ayala Mashiah-Yaakovi, 2014. "Subgame perfect equilibria in stopping games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 89-135, February.
    20. Oscar Volij & Casilda Lasso de la Vega, 2016. "The Value Of A Draw In Quasi-Binary Matches," Working Papers 1601, Ben-Gurion University of the Negev, Department of Economics.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00595481. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.