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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

This paper models a penalty kicker’s problem in football. The study takes into consideration the 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 is 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) is obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method is 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 Technology, Faculty of Management, vol. 3, pages 17-27.
  • Handle: RePEc:wut:journl:v:3:y:2018:p:17-27:id:1375
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    References listed on IDEAS

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    1. Carlos Gracia-Lázaro & Luis Mario Floría & Yamir Moreno, 2017. "Cognitive Hierarchy Theory and Two-Person Games," Games, MDPI, Open Access Journal, vol. 8(1), pages 1-18, January.
    2. 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.
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    4. Roman Szostek, 2011. "An effective system of sports competition management," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 1, pages 65-75.
    5. Mamoru Kaneko & Shuige Liu, 2015. "Elimination of dominated strategies and inessential players," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 1, pages 33-54.
    6. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 395-415.
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