The penalty-kick game under incomplete information

Arbeitspapier

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).

Object Details

• ISBN: 978-987-1062-75-1
• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Serie Documentos de Trabajo ; No. 487

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Sports; Gambling; Restaurants; Recreation; Tourism
• Subject: soccer penalty kicks ; mixed strategies ; Bayesian equilibrium ; incomplete information ; Fußballsport ; Unvollkommene Information ; Bayes-Statistik

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Coloma, Germán
• Event: Veröffentlichung
• (who): Universidad del Centro de Estudios Macroeconómicos de Argentina (UCEMA)
• (where): Buenos Aires
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/84428
• Last update: 10.03.2025, 11:42 AM CET