Abstract. Soccer is the world's number one sport, known for its fierce rivalries and full of surprises. Especially in important international competitions, such as the World Cup and the European Championships, matches are often about national honor and the expectations of millions of fans. Penalty kicks are a common punishment in soccer, where the goalkeeper and the shooter are pitted against each other in a one-on-one confrontation. Penalty kicks, because of their simplicity of confrontation, have a breath-taking tension and excitement, and most of the victory depends on the decision-making confrontation between the shooter and the goalkeeper. Game theory is an important tool for studying how participants make decisions to maximize their own gains in situations of conflict and competition. In order to study how the goalkeeper saves most effectively, this paper analyzes the penalty shot from the perspective of game theory, and obtains the optimal solution for the goalkeeper's save direction in a simplified situation by calculating the Nash equilibrium under mixed strategies.
Read full abstract