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Equilibrium play in matches: Binary Markov games

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  • 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
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    References listed on IDEAS

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    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. 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.
    5. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
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    Cited by:

    1. González-Díaz, Julio & Gossner, Olivier & Rogers, Brian W., 2012. "Performing best when it matters most: Evidence from professional tennis," Journal of Economic Behavior & Organization, Elsevier, vol. 84(3), pages 767-781.
    2. Martin G. Kocher & Marc V. Lenz & Matthias Sutter, 2010. "Psychological pressure in competitive environments: Evidence from a randomized natural experiment: Comment," NCER Working Paper Series 55, National Centre for Econometric Research.
    3. 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.
    4. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," CORE Discussion Papers 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Loertscher, Simon, 2013. "Rock–Scissors–Paper and evolutionarily stable strategies," Economics Letters, Elsevier, vol. 118(3), pages 473-474.
    6. 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.
    7. Martin G. Kocher & Marc V. Lenz & Matthias Sutter, 2012. "Psychological Pressure in Competitive Environments: New Evidence from Randomized Natural Experiments," Management Science, INFORMS, vol. 58(8), pages 1585-1591, August.
    8. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.
    9. Bizzozero, Paolo & Flepp, Raphael & Franck, Egon, 2016. "The importance of suspense and surprise in entertainment demand: Evidence from Wimbledon," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 47-63.
    10. Romain Gauriot & Lionel Page, 2014. "Does success breed success? A quasi-experiment on strategic momentum in dynamic contests," QuBE Working Papers 028, QUT Business School.
    11. Bradley J. Ruffle & Oscar Volij, 2016. "First-mover advantage in best-of series: an experimental comparison of role-assignment rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 933-970, November.
    12. Shih-Hsun Hsu & Chen-Ying Huang & Cheng-Tao Tang, 2007. "Minimax Play at Wimbledon: Comment," American Economic Review, American Economic Association, vol. 97(1), pages 517-523, March.

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