Equilibrium play in matches: Binary Markov games

Mark Walker, John Wooders, Rabah Amir

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)487-502
Number of pages16
JournalGames and Economic Behavior
Issue number2
StatePublished - Mar 2011


  • Game theory and sports
  • Minimax
  • Stochastic games
  • Strictly competitive games
  • Tennis

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics


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