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).


    Access

    Download


    Export, share and cite



    Title :

    The penalty-kick game under incomplete information


    Contributors:

    Publication date :

    2012-01-01


    Remarks:

    RePEc:cem:doctra:487


    Type of media :

    Paper


    Type of material :

    Electronic Resource


    Language :

    English



    Classification :

    DDC:    330 / 629




    Spacecraft differential game interception control method under incomplete information

    YE DONG / TANG XU / XIAO YAN et al. | European Patent Office | 2023

    Free access

    MADRL-based UAV swarm non-cooperative game under incomplete information

    WANG, Ershen / LIU, Fan / HONG, Chen et al. | Elsevier | 2024

    Free access

    KICK SCOOTER

    DEGN STEFAN | European Patent Office | 2019

    Free access

    KICK BOARD

    YOON EEM SIK | European Patent Office | 2016

    Free access

    Kick Scooter

    PETUTSCHNIG HUBERT | European Patent Office | 2016

    Free access