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).
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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:
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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.:
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"Professionals Play Minimax,"
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"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.
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