Nash equilibrium and tennis serve performance: a game theory analysis

Abstract

ABSTRACT This study presents an in-depth analysis of the serve in men’s singles tennis matches at Wimbledon based on game theory, with the quantitative tool of the stroke performance relevance (SPR) model. This model quantifies tennis tactics more precisely, taking “each stroke” as the observation unit, and it includes scoring, losing points, and sequential information. Unlike traditional methods that consider “each point”, the SPR metrics captures the role of specific technical actions throughout the match more comprehensively. While standard serve data like aces and double faults have no significant impact on match outcomes, the serve SPR index does. In a game matrix model with two pure strategy Nash equilibria, both the winner and loser show higher SPR indices than those with fewer equilibria. Winners consistently exhibited a higher serve SPR index, indicating that the two pure strategy Nash equilibria significantly influenced match outcomes on grass courts. This underscores the role of tactical strategies and Nash equilibrium in determining match results, offering scientific and theoretical support for tennis athletes’ and coaches’ tactics.