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).


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    Titel :

    The penalty-kick game under incomplete information


    Beteiligte:

    Erscheinungsdatum :

    2012-01-01


    Anmerkungen:

    RePEc:cem:doctra:487


    Medientyp :

    Paper


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



    Klassifikation :

    DDC:    330 / 629




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