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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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 71 (2011)
Issue (Month): 2 (March)
Pages: 487-502

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Handle: RePEc:eee:gamebe:v:71:y:2011:i:2:p:487-502

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Stochastic games Minimax Strictly competitive games Game theory and sports Tennis;

References

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  1. 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.
  2. 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.
  3. 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.
  4. Tijs, S.H. & Vrieze, O.J., 1986. "On the existence of easy initial states for undiscounted stochastic games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154263, Tilburg University.
  5. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  6. Nicolas Vieille, 2002. "Stochastic Games : recent results," Working Papers hal-00242996, HAL.
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Cited by:
  1. Kocher, Martin G. & Lenz, Marc V. & Sutter, Matthias, 2010. "Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment: Comment," IZA Discussion Papers 4846, Institute for the Study of Labor (IZA).
  2. 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.
  3. Loertscher, Simon, 2013. "Rock–Scissors–Paper and evolutionarily stable strategies," Economics Letters, Elsevier, vol. 118(3), pages 473-474.
  4. 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.
  5. 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).

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