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

## TL;DR

This paper introduces a mean field game framework for autonomous vehicle velocity control, enabling scalable, rational decision-making that bridges microscopic behaviors and macroscopic traffic flow, and improves traffic jam mitigation.

## Contribution

It develops a systematic mean field game approach for AV velocity control, linking microscopic agent behaviors with macroscopic traffic models, and demonstrates improved traffic flow management.

## Key findings

- MFG-based controller reduces traffic jams faster than LWR-based controller.
- The framework provides a new traffic flow theory for autonomous vehicles.
- Systematic micro-macro modeling of AV behaviors and traffic dynamics.

## Abstract

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.