The penalty-kick game under incomplete information
This 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).
|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
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.:
- Ignacio Palacios-Huerta, 2003.
"Professionals Play Minimax,"
Review of Economic Studies,
Oxford University Press, vol. 70(2), pages 395-415.
- 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, The North American Association of Sports Economists, vol. 12(1), pages 81-105, February.
When requesting a correction, please mention this item's handle: RePEc:cem:doctra:487. See general information about how to correct material in RePEc.
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.