# A Non-Cooperative Game Approach to Autonomous Racing

arXiv: https://arxiv.org/abs/1712.03913 · HTML: https://mlsanity.com/paper/1712.03913/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2017.

## Built on by (most cited first, 19 of 19)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [Deep Interactive Motion Prediction and Planning: Playing Games with Motion Prediction Models](https://mlsanity.com/paper/2204.02392/) (2022)
- [Deep Latent Competition: Learning to Race Using Visual Control Policies in Latent Space](https://mlsanity.com/paper/2102.09812/) (2021)
- [Learning Interactive Driving Policies via Data-driven Simulation](https://mlsanity.com/paper/2111.12137/) (2021)
- [A Super-human Vision-based Reinforcement Learning Agent for Autonomous Racing in Gran Turismo](https://mlsanity.com/paper/2406.12563/) (2024)
- [Indy Autonomous Challenge -- Autonomous Race Cars at the Handling Limits](https://mlsanity.com/paper/2202.03807/) (2022)
- [iPLAN: Intent-Aware Planning in Heterogeneous Traffic via Distributed Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2306.06236/) (2023)
- [A Game-Theoretic Framework for Joint Forecasting and Planning](https://mlsanity.com/paper/2308.06137/) (2023)
- [Sampling-Based Motion Planning with Online Racing Line Generation for Autonomous Driving on Three-Dimensional Race Tracks](https://mlsanity.com/paper/2403.18643/) (2024)
- [Search-Based Task and Motion Planning for Hybrid Systems: Agile Autonomous Vehicles](https://mlsanity.com/paper/2301.10384/) (2023)
- [Collaborative Navigation and Manipulation of a Cable-towed Load by Multiple Quadrupedal Robots](https://mlsanity.com/paper/2206.14424/) (2022)
- [Trajectory Planning Using Reinforcement Learning for Interactive Overtaking Maneuvers in Autonomous Racing Scenarios](https://mlsanity.com/paper/2404.10658/) (2024)
- [Track based Offline Policy Learning for Overtaking Maneuvers with Autonomous Racecars](https://mlsanity.com/paper/2107.09782/) (2021)
- [Linear Differential Games for Cooperative Behavior Planning of Autonomous Vehicles Using Mixed-Integer Programming](https://mlsanity.com/paper/2109.15122/) (2021)
- [Adaptive Decision-Making for Autonomous Vehicles: A Learning-Enhanced Game-Theoretic Approach in Interactive Environments](https://mlsanity.com/paper/2402.11467/) (2024)
- [Fair Play in the Fast Lane: Integrating Sportsmanship into Autonomous Racing Systems](https://mlsanity.com/paper/2503.03774/) (2025)
- [Game-theoretic Objective Space Planning](https://mlsanity.com/paper/2209.07758/) (2022)
- [Reinforcement Learning-based Dynamic Adaptation for Sampling-Based Motion Planning in Agile Autonomous Driving](https://mlsanity.com/paper/2510.10567/) (2025)
- [Choose Your Game Wisely: Measuring Game-Theoretic Structures in Real-World Vehicle Interactions](https://mlsanity.com/paper/2608.25917/) (2026)

## Abstract (arXiv)

We consider autonomous racing of two cars and present an approach to formulate racing decisions as a non-cooperative non-zero-sum game. We design three different games where the players aim to fulfill static track constraints as well as avoid collision with each other; the latter constraint depends on the combined actions of the two players. The difference between the games are the collision constraints and the payoff. In the first game collision avoidance is only considered by the follower, and each player maximizes their own progress towards the finish line. We show that, thanks to the sequential structure of this game, equilibria can be computed through an efficient sequential maximization approach. Further, we show these actions, if feasible, are also a Stackelberg and Nash equilibrium in pure strategies of our second game where both players consider the collision constraints. The payoff of our third game is designed to promote blocking, by additionally rewarding the cars for staying ahead at the end of the horizon. We show that this changes the Stackelberg equilibrium, but has a minor influence on the Nash equilibria. For online implementation, we propose to play the games in a moving horizon fashion, and discuss two methods for guaranteeing feasibility of the resulting coupled repeated games. Finally, we study the performance of the proposed approaches in simulation for a set-up that replicates the miniature race car tested at the Automatic Control Laboratory of ETH Zurich. The simulation study shows that the presented games can successfully model different racing behaviors and generate interesting racing situations.