Minimax Outside the Top-5

Abstract

Is the behavior of people consistent with the predictions of the Nash equilibrium and, in particular, the minimax theorem? This paper explores how close is the behavior of not-so-skilled and not-so-experienced professional players to the minimax predictions in a natural setting. In particular, I test the hypotheses that, first, success rates are the same across strategies for all the players, and, second, strategic choices of both opponents do not demonstrate inertia and are serially independent. To address the question, I use a novel dataset on the universe of penalty kicks performed by the professional players representing a soccer league of moderate quality. I show that the behavior of players is broadly consistent with the predictions of the minimax theorem despite the lower quality of the league.

Keywords: Nash Equilibrium, Minimax, Skills, Randomization, Inertia

JEL Classification: C12, C72, D83, D91, Z20