# A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games

arXiv: https://arxiv.org/abs/1903.06053 · HTML: https://mlsanity.com/paper/1903.06053/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [Milestones in Autonomous Driving and Intelligent Vehicles Part I: Control, Computing System Design, Communication, HD Map, Testing, and Human Behaviors](https://mlsanity.com/paper/2305.11239/) (2023)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [A Survey on Approximate Edge AI for Energy Efficient Autonomous Driving Services](https://mlsanity.com/paper/2304.14271/) (2023)
- [Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm](https://mlsanity.com/paper/2405.08005/) (2024)
- [Exploration noise for learning linear-quadratic mean field games](https://mlsanity.com/paper/2107.00839/) (2021)
- [Deep Learning for Mean Field Games with non-separable Hamiltonians](https://mlsanity.com/paper/2301.02877/) (2023)
- [Evidence and quantification of cooperation of driving agents in mixed traffic flow](https://mlsanity.com/paper/2408.07297/) (2024)
- [Networked Communication for Decentralised Agents in Mean-Field Games](https://mlsanity.com/paper/2306.02766/) (2023)
- [Self-Interest and Systemic Benefits: Emergence of Collective Rationality in Mixed Autonomy Traffic Through Deep Reinforcement Learning](https://mlsanity.com/paper/2511.04883/) (2025)

## Abstract (arXiv)

This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our goal is to design future AVs as rational, utility-optimizing agents that continuously select optimal velocity over a period of planning horizon. With a large number of interacting AVs, this design problem can become computationally intractable. This paper aims to tackle such a challenge by employing mean field approximation and deriving a mean field game (MFG) as the limiting differential game with an infinite number of agents. The proposed micro-macro model allows one to define individuals on a microscopic level as utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Different from existing studies on the application of MFG to traffic flow models, the present study offers a systematic framework to apply MFG to autonomous vehicle velocity control. The MFG-based AV controller is shown to mitigate traffic jam faster than the LWR-based controller. MFG also embodies classical traffic flow models with behavioral interpretation, thereby providing a new traffic flow theory for AVs.