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Equilibrium play in matches: Binary Markov games

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Nicolas Vieille, 2002. "Stochastic Games : recent results," Working Papers hal-00242996, HAL.
  2. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  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. 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.
  6. 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.
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