IDEAS home Printed from https://ideas.repec.org/a/wut/journl/v3y2018p17-27id1375.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://ord.pwr.edu.pl/assets/papers_archive/1375%20-%20published.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.5277/ord180302?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Ignacio Palacios-Huerta & Oscar Volij, 2008. "Experientia Docet: Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 76(1), pages 71-115, January.
    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. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kocher, Martin G. & Lenz, Marc V. & Sutter, Matthias, 2010. "Psychological pressure in competitive environments: Evidence from a randomized natural experiment: Comment," Discussion Papers in Economics 11445, University of Munich, Department of Economics.
    2. 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.
    3. Van Essen, Matt & Wooders, John, 2015. "Blind stealing: Experience and expertise in a mixed-strategy poker experiment," Games and Economic Behavior, Elsevier, vol. 91(C), pages 186-206.
    4. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    5. Heifetz, Aviad & Heller, Ruth & Ostreiher, Roni, 2021. "Do Arabian babblers play mixed strategies in a “volunteer’s dilemma”?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    6. Steven D. Levitt & John A. List & David H. Reiley, 2010. "What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 78(4), pages 1413-1434, July.
    7. Yuval Salant & Jörg L. Spenkuch, 2021. "Complexity and Choice," CESifo Working Paper Series 9239, CESifo.
    8. Kenneth Kovash & Steven D. Levitt, 2009. "Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League," NBER Working Papers 15347, National Bureau of Economic Research, Inc.
    9. Alexander Cotte Poveda, Julian Gutierrez López, 2016. "Incertidumbre y riesgo en los cobros desde el punto penal: un análisis aplicando la teoría de juegos," Revista CIFE, Universidad Santo Tomás, March.
    10. Spiliopoulos, Leonidas, 2013. "Beyond fictitious play beliefs: Incorporating pattern recognition and similarity matching," Games and Economic Behavior, Elsevier, vol. 81(C), pages 69-85.
    11. Spenkuch, Jörg, 2014. "Backward Induction in the Wild: Evidence from the U.S. Senate," MPRA Paper 58766, University Library of Munich, Germany.
    12. Thomas Dohmen & Hendrik Sonnabend, 2018. "Further Field Evidence for Minimax Play," Journal of Sports Economics, , vol. 19(3), pages 371-388, April.
    13. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    14. Yoshitaka Okano, 2016. "Re-examination of team’s play in a mixed-strategy game experiment," Applied Economics Letters, Taylor & Francis Journals, vol. 23(8), pages 601-604, May.
    15. Okano, Yoshitaka, 2013. "Minimax play by teams," Games and Economic Behavior, Elsevier, vol. 77(1), pages 168-180.
    16. Jeanine Miklós-Thal & Hannes Ullrich, 2016. "Career Prospects and Effort Incentives: Evidence from Professional Soccer," Management Science, INFORMS, vol. 62(6), pages 1645-1667, June.
    17. Steven Levitt & John List & David Reiley, 2010. "What happens in the field stays in the field: Professionals do not play minimax in laboratory experiments," Artefactual Field Experiments 00080, The Field Experiments Website.
    18. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
    19. Etan A. Green & Justin M. Rao & David Rothschild, 2019. "A Sharp Test of the Portability of Expertise," Management Science, INFORMS, vol. 67(6), pages 2820-2831, June.
    20. Leonidas Spiliopoulos, 2018. "Randomization and serial dependence in professional tennis matches: Do strategic considerations, player rankings and match characteristics matter?," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(5), pages 413-427, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wut:journl:v:3:y:2018:p:17-27:id:1375. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Adam Kasperski (email available below). General contact details of provider: https://edirc.repec.org/data/iopwrpl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.