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On the one-shot two-person zero-sum game in football from a penalty kicker’s perspective

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  • Virtue Ekhosuehi

Abstract

A penalty kicker’s problem in football has been modelled. The study took into consideration different directions in which the ball can be struck and goalkeepers’ success at defending shots. The strategic form of the game that can be used to predict how the kicker should optimally randomise his strategies has been modelled as a non-linear game-theoretic problem from a professional kicker’s viewpoint. The equilibrium of the game (i.e., the pair of mutually optimal mixed strategies) was obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method was adopted to solve this problem. The optimal solution to the game indicates that the kicker never chooses to kick the ball off target, to the goalpost or to the crossbar, but rather chooses to kick the ball in the opposite direction to the one where the goalkeeper is most likely to successfully defend from past history.

Suggested Citation

  • Virtue Ekhosuehi, 2018. "On the one-shot two-person zero-sum game in football from a penalty kicker’s perspective," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(3), pages 17-27.
    • Handle: RePEc:wut:journl:v:3:y:2018:p:17-27:id:1375
    DOI: 10.5277/ord180302
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    References listed on IDEAS

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    1. Ignacio Palacios-Huerta & Oscar Volij, 2008. "Experientia Docet: Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 76(1), pages 71-115, January.
    2. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    3. Carlos Gracia-Lázaro & Luis Mario Floría & Yamir Moreno, 2017. "Cognitive Hierarchy Theory and Two-Person Games," Games, MDPI, vol. 8(1), pages 1-18, January.
    4. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
    5. Roman Szostek, 2011. "An effective system of sports competition management," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 65-75.
    6. Mamoru Kaneko & Shuige Liu, 2015. "Elimination of dominated strategies and inessential players," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(1), pages 33-54.
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