Bayesian Equilibria in the Penalty-Kick Game


This paper describes a model of a soccer game between a goalkeeper and a kicker, in which each player attempts to score or avoid a goal. There are two alternative strategies for each player in this version of the penalty-kick game (connected to where they choose to kick or move themselves) and there is also uncertainty about the kicker’s type (with two possible types of kicker). We apply the concept of Bayesian equilibrium to find a solution for this game, and we discover that one of the kicker types will typically play a mixed strategy, while the other will adopt a pure strategy. We find that when we compare this equilibrium to the analogous Nash equilibria under complete knowledge, the anticipated scoring probability rises (so that, on average, the goalkeeper is worse off).

Author (S) Details

Germán Coloma
CEMA University, Buenos Aires, Argentina.

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