Estimating performance characteristics through observed nash equilibria

Abstract

This article uses simple game models to investigate penalty kick shootouts in soccer. As opposed to existing research, which mainly focuses on empirical/experimental problems, the game itself is the main focus here. Interesting ndings include a proposed Nash equilibrium invariance for possible preference di erences between penalty kick Executors and Keepers as well as identi cation and demonstration of how game models may be used in order to estimate player performance characteristics through observed Nash equilibria outcomes. A non-mixed strategy Nash equilibrium is also shown to be possible with potential interesting consequences for goal keepers.