IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v71y2011i2p487-502.html
   My bibliography  Save this article

Equilibrium play in matches: Binary Markov games

Author

Listed:
  • Walker, Mark
  • Wooders, John
  • Amir, Rabah

Abstract

We study two-person extensive form games, or "matches," in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in "point games." We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided.

Suggested Citation

  • Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.
    • Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:487-502
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(10)00072-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vieille, Nicolas, 2002. "Stochastic games: Recent results," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 48, pages 1833-1850, Elsevier.
    2. Wooders, John & Shachat, Jason M., 2001. "On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 342-363, February.
    3. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    4. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    5. Nicolas Vieille, 2000. "Two-player stochastic games I: A reduction," Post-Print hal-00481401, HAL.
    6. 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.
    7. S. H. Tijs & O. J. Vrieze, 1986. "On the Existence of Easy Initial States for Undiscounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 11(3), pages 506-513, August.
    8. Tijs, S.H. & Vrieze, O.J., 1986. "On the existence of easy initial states for undiscounted stochastic games," Other publications TiSEM eb99a01d-30d5-456c-8aba-6, Tilburg University, School of Economics and Management.
    9. Nicolas Vieille, 2000. "Two-player stochastic games II: The case of recursive games," Post-Print hal-00481416, HAL.
    Full references (including those not matched with items on IDEAS)

    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. Casilda Lasso de la Vega & Oscar Volij, 2020. "The value of a draw," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1023-1044, November.
    2. 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.
    3. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.
    5. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    6. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    7. Geng, Sen & Peng, Yujia & Shachat, Jason & Zhong, Huizhen, 2015. "Adolescents, cognitive ability, and minimax play," Economics Letters, Elsevier, vol. 128(C), pages 54-58.
    8. Van Essen, Matt & Wooders, John, 2015. "Blind stealing: Experience and expertise in a mixed-strategy poker experiment," Games and Economic Behavior, Elsevier, vol. 91(C), pages 186-206.
    9. Okano, Yoshitaka, 2013. "Minimax play by teams," Games and Economic Behavior, Elsevier, vol. 77(1), pages 168-180.
    10. Maria Montero & Alex Possajennikov & Martin Sefton & Theodore Turocy, 2013. "Majoritarian Contests with Asymmetric Battlefields: An Experiment," Discussion Papers 2013-12, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    11. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
    12. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.
    13. Boros, E. & Gurvich, V., 2003. "On Nash-solvability in pure stationary strategies of finite games with perfect information which may have cycles," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 207-241, October.
    14. Dimitris Batzilis & Sonia Jaffe & Steven Levitt & John A. List & Jeffrey Picel, 2019. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games," Games, MDPI, vol. 10(2), pages 1-34, April.
    15. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.
    16. Venel, Xavier, 2021. "Regularity of dynamic opinion games," Games and Economic Behavior, Elsevier, vol. 126(C), pages 305-334.
    17. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.
    18. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Scroggin, Steven, 2007. "Exploitable actions of believers in the "law of small numbers" in repeated constant-sum games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 219-235, March.
    20. Maria Montero & Alex Possajennikov & Martin Sefton & Theodore Turocy, 2016. "Majoritarian Blotto contests with asymmetric battlefields: an experiment on apex games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 55-89, January.

    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:eee:gamebe:v:71:y:2011:i:2:p:487-502. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.