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Do soccer players play the mixed-strategy Nash equilibrium?

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  • Azar, Ofer H.
  • Bar-Eli, Michael

Abstract

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not.

Suggested Citation

  • Azar, Ofer H. & Bar-Eli, Michael, 2009. "Do soccer players play the mixed-strategy Nash equilibrium?," MPRA Paper 20964, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:20964
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    References listed on IDEAS

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    Cited by:

    1. Mario Lackner & Hendrik Sonnabend, 2017. "Coping with advantageous inequity - Field evidence from professional penalty kicking," Economics working papers 2017-21, Department of Economics, Johannes Kepler University Linz, Austria.
    2. Duffy, Sean & Naddeo, JJ & Owens, David & Smith, John, 2016. "Cognitive load and mixed strategies: On brains and minimax," MPRA Paper 71878, University Library of Munich, Germany.
    3. 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.
    4. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2014. "Minimax on the gridiron: Serial correlation and its effects on outcomes in the National Football League," MPRA Paper 58907, University Library of Munich, Germany.

    More about this item

    Keywords

    Soccer; Football; MSNE; Mixed-strategies; Mixed-strategy Nash equilibrium; Sports; Penalty kicks;

    JEL classification:

    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D00 - Microeconomics - - General - - - General
    • C93 - Mathematical and Quantitative Methods - - Design of Experiments - - - Field Experiments
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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