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Game Theory in Formula 1: Multi-agent Physical and Strategical Interactions

This paper presents an optimization framework to model Formula 1 racing dynamics, where multiple cars interact physically and strategically. Aerodynamic wake effects, trajectory optimization, and energy management are integrated by means of physical models. 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. By incorporating a physically accurate interaction model and accounting for the optimal responses of competing agents, our approach reveals typical Formula 1 strategic behaviors. The proposed methodology closes the gap between theoretical game theory and real-world racing, with potential applications in motorsport engineering and autonomous racing.

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