Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/84428
Authors: 
Coloma, Germán
Year of Publication: 
2012
Series/Report no.: 
Serie Documentos de Trabajo, Universidad del CEMA: Área: economía 487
Abstract: 
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).
Subjects: 
soccer penalty kicks
mixed strategies
Bayesian equilibrium
incomplete information
JEL: 
C72
L83
ISBN: 
978-987-1062-75-1
Document Type: 
Working Paper

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