Game Theory in Formula 1: From Physical to Strategic Interactions

Abstract

This paper presents an optimization framework to model multi-agent racing dynamics. By incorporating physically accurate interaction models and accounting for the optimal responses of competing agents, our approach reveals strategic behaviors typical of motorsport. Aerodynamic wake effects, trajectory optimization, and energy management are captured and evaluated on a representative case study, based on a Formula 1 scenario. We describe the minimum lap time problem with two agents as either a Nash or a Stackelberg game, and by employing the Karush-Kuhn-Tucker conditions during the problem formulation, we recover the structure of a nonlinear program. In addition, we introduce an algorithm to refine local Stackelberg solutions, using the Nash costs as upper bounds. The resulting strategies are analyzed through case studies. We examine the impact of slipstreaming on trajectory selection in corners, straights, and high-speed sections, while also identifying optimal overtaking locations based on energy allocation strategies. Exploiting the structural similarities of the game formulations, we are able to compare symmetric and hierarchical strategies to analyze competitive racing dynamics. The proposed methodology closes the gap between theoretical game theory and practical applications, with relevance in multi-agent systems with coupled nonlinear dynamics.