Nash Equilibrium and Penalty Kicks Outside the Top-5 : It Is Not As Bad As You Think

Is the behavior of people consistent with the predictions of the Nash equilibrium and, in particular, the Minimax hypothesis? The existing literature have not reached a consensus about the answer to this question. This paper studies whether the soccer players involved in a penalty kick behave themselves according to the predictions of the equilibrium play. Using a novel dataset consisting of 1679 penalty kicks, I show that the behavior of players is consistent with the Minimax hypothesis despite they represent a league that is of moderate quality in terms of skills. However, when I make use of the Kolmogorov-Smirnov test based on the randomized Fisher exact test — a test that is more powerful than any existing one used in the prior literature on the Minimax behavior — I call into question the result that success rates are identical across players' strategies, a necessary prediction of the Minimax hypothesis. This suggests that the existing positive results should be taken with a grain of salt