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The value of a draw

Author

Listed:
  • Casilda Lasso de la Vega

    (University of the Basque Country)

  • Oscar Volij

    (Ben-Gurion University of the Negev)

Abstract

We model a match as a recursive zero-sum game with three possible outcomes: Player 1 wins, player 2 wins, or there is a draw. We focus on matches whose point games also have three possible outcomes: Player 1 scores the point, player 2 scores the point, or the point is drawn in which case the point game is repeated. We show that a value of a draw can be attached to each state so that an easily computed stationary equilibrium exists in which players’ strategies can be described as minimax behavior in the point games induced by these values.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:70:y:2020:i:4:d:10.1007_s00199-018-1140-x
    DOI: 10.1007/s00199-018-1140-x
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    References listed on IDEAS

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    1. 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.
    2. Jose Apesteguia & Ignacio Palacios-Huerta, 2010. "Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 100(5), pages 2548-2564, December.
    3. González-Díaz, Julio & Palacios-Huerta, Ignacio, 2016. "Cognitive performance in competitive environments: Evidence from a natural experiment," Journal of Public Economics, Elsevier, vol. 139(C), pages 40-52.
    4. Romain Gauriot & Lionel Page & John Wooders, 2016. "Nash at Wimbledon: Evidence from Half a Million Serves," QuBE Working Papers 046, QUT Business School.
    5. 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.
    6. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    7. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    8. Schwalbe, Ulrich & Walker, Paul, 2001. "Zermelo and the Early History of Game Theory," Games and Economic Behavior, Elsevier, vol. 34(1), pages 123-137, January.
    9. 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.
    10. Nicolas Vieille, 2000. "Two-player stochastic games II: The case of recursive games," Post-Print hal-00481416, HAL.
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    Cited by:

    1. Rabah Amir, 2020. "Special Issue: Supermodularity and Monotonicity in Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 907-911, November.

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    More about this item

    Keywords

    Matches; Stochastic games; Recursive games; Draws;
    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

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