Equilibrium play in matches

Binary Markov games

Mark Walker, John Wooders, Rabah Amir

    Research output: Contribution to journalArticle

    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.

    Original languageEnglish (US)
    Pages (from-to)487-502
    Number of pages16
    JournalGames and Economic Behavior
    Volume71
    Issue number2
    DOIs
    StatePublished - Mar 1 2011

    Fingerprint

    Nash equilibrium
    Minimax
    Extensive form games
    Monotonicity
    Tennis

    Keywords

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

    ASJC Scopus subject areas

    • Economics and Econometrics
    • Finance

    Cite this

    Equilibrium play in matches : Binary Markov games. / Walker, Mark; Wooders, John; Amir, Rabah.

    In: Games and Economic Behavior, Vol. 71, No. 2, 01.03.2011, p. 487-502.

    Research output: Contribution to journalArticle

    Walker, Mark ; Wooders, John ; Amir, Rabah. / Equilibrium play in matches : Binary Markov games. In: Games and Economic Behavior. 2011 ; Vol. 71, No. 2. pp. 487-502.
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