Game Theory in Formula 1: From Physical to Strategic Interactions

Jul 16, 2026

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This paper develops an optimization framework for multi-agent racing dynamics that unifies physically accurate interaction modeling with strategic decision-making. Aerodynamic wake effects, trajectory optimization, and energy management are jointly captured and assessed in a representative Formula 1 scenario. The minimum lap time problem for two agents is formulated as either a Nash or a Stackelberg game, with Karush-Kuhn-Tucker conditions recovering a nonlinear program structure. A refinement algorithm leverages Nash costs as upper bounds, enabling case-study analysis of slipstreaming and energy-guided overtaking, and comparisons of symmetric versus hierarchical strategies.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

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Graphical Abstract Game Theory in Formula 1: From Physical to Strategic Interactions Giona Fieni, Marc-Philippe Neumann, Francesca Furia, Alessandro Caucino, Alberto Cerofolini, Vittorio Ravaglioli, Christopher H. Onder [ ee ss . SY] 13 Jul 2026 arXiv :2503 .05421v5 | Physical interactions and energy management | | --- | | | | Game-theoretic formulations<br>Stackelberg game | | | --- | --- | Strategic interactions Game Theory in Formula 1: From Physical to Strategic Interactions Giona Fienia,∗, Marc-Philippe Neumanna , Francesca Furiab , Alessandro Caucinoa , Alberto Cerofolinic , Vittorio Ravagliolib , Christopher H. Ondera a Institute for Dynamic Systems and Control, ETH Zürich, 8092 Zürich, Switzerland b Department of Industrial Engineering, Università di Bologna, 47121 Forlì, Italy c Power Unit Performance and Control Strategies Group, Ferrari S.p.A., 41053 Maranello, Italy 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. Keywords: Energy management, Formula 1, hybrid-electric, multi-agent, physical interactions, game theory, nonlinear programming. 1. Introduction Competitive motorsport racing drives innovation. Every year, the teams strive to improve and update their cars to achieve maximum performance. From aerodynamics to vehicle dynamics and power units (PUs), the limits of engineering are continuously pushed. Despite the technical innovations, the human component is still a central pillar of motorsport. Pilots exploit years of training and experience to perfectly master the vehicle, for instance by choosing the right trajectory leveraging the vehicle’s dynamics. They have to take decisions in a fraction of a second by considering the presence, the actions and the response of competitors. Most research to date has been focused on the optimization of a single vehicle. However, the presence of other cars on the track introduces complex interactions of a both physical and strategic nature. In particular, the aerodynamic response of a vehicle is significantly influenced by the turbulence generated by a leading car. This wake effect reduces aerodynamic drag, enabling energy savings and allowing the trailing vehicle to achieve higher velocity peaks. On the other hand, the reduction in drag comes with a decrease in downforce, which can negatively impact cornering performance. While the former effect provides a competitive advantage, particularly on straights, ∗ Corresponding author. Email address: [gfieni@idsc.mavt.ethz.ch](gfieni@idsc.mavt.ethz.ch) (Giona Fieni) the latter poses a challenge in high-speed corners. These tradeoffs affect strategical decisions, such as overt

FAQs

What problem does the paper address in multi-agent Formula 1 racing?

It addresses minimum lap time and strategy decisions in a multi-agent setting by modeling coupled aerodynamic interactions, trajectory optimization, and energy management together rather than separately.

How are two-agent strategies modeled in the paper?

The minimum lap time problem for two agents is expressed either as a Nash game or as a Stackelberg game, and the formulation uses Karush-Kuhn-Tucker conditions to obtain a nonlinear programming structure.

What does the paper conclude about overtaking and slipstreaming?

Case studies analyze how slipstreaming influences trajectory selection in corners, straights, and high-speed sections, and it identifies overtaking locations using energy allocation strategies.

Jul 16, 2026

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