The penalty-kick game under incomplete information
AbstractThis paper presents a model of the penalty-kick game between a soccer goalkeeper and a kicker, in which there is uncertainty about the kicker’s type (and there are two possible types of kicker). To find a solution for this game we use the concept of Bayesian equilibrium, and we find that, typically, one of the kicker’s types will play a mixed strategy while the other type will choose a pure strategy (or, sometimes, a “restricted mixed strategy”). The model has a simpler version in which the players can only choose between two strategies (right and left), and a more complex version in which they can also choose a third strategy (the center of the goal). Comparing the incomplete-information Bayesian equilibria with the corresponding complete-information Nash equilibria, we find that in all cases the expected scoring probability increases (so that, on average, the goalkeeper is worse off under incomplete information). The three-strategy model is also useful to explain why it could be optimal for a goal keeper never to choose the center of the goal (although at the same time there were some kickers who always chose to shoot to the center).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Universidad del CEMA in its series CEMA Working Papers: Serie Documentos de Trabajo. with number 487.
Length: 32 pages
Date of creation: May 2012
Date of revision:
Contact details of provider:
Postal: Av. Córdoba 374, (C1054AAP) Capital Federal
Phone: (5411) 6314-3000
Fax: (5411) 4314-1654
Web page: http://www.cema.edu.ar/publicaciones/doc_trabajo.html
More information through EDIRC
soccer penalty kicks; mixed strategies; Bayesian equilibrium; incomplete information;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-07-14 (All new papers)
- NEP-CTA-2012-07-14 (Contract Theory & Applications)
- NEP-GTH-2012-07-14 (Game Theory)
- NEP-HPE-2012-07-14 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bar-Eli, Michael & Azar, Ofer H. & Ritov, Ilana & Keidar-Levin, Yael & Schein, Galit, 2007.
"Action bias among elite soccer goalkeepers: The case of penalty kicks,"
Journal of Economic Psychology,
Elsevier, vol. 28(5), pages 606-621, October.
- Bar-Eli, Michael & Azar, Ofer H. & Ritov, Ilana & Keidar-Levin, Yael & Schein, Galit, 2005. "Action bias among elite soccer goalkeepers: The case of penalty kicks," MPRA Paper 4477, University Library of Munich, Germany.
- Florian Baumann & Tim Friehe & Michael Wedow, 2011. "General Ability and Specialization: Evidence From Penalty Kicks in Soccer," Journal of Sports Economics, , vol. 12(1), pages 81-105, February.
- Ignacio Palacios-Huerta, 2003.
"Professionals Play Minimax,"
Review of Economic Studies,
Oxford University Press, vol. 70(2), pages 395-415.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Valeria Dowding).
If references are entirely missing, you can add them using this form.