Linearly Solvable Mean-Field Road Traffic Games

TL;DR

This paper models urban traffic with many drivers using mean-field games, showing that congestion can be mitigated through a logarithmic tax, and that equilibrium solutions are efficiently computable via linear systems.

Contribution

It introduces a novel mean-field game framework for traffic with a logarithmic congestion tax, leading to linearly solvable Markov decision processes for equilibrium computation.

Findings

Equilibrium can be found by solving a linear system.

The model effectively captures strategic driver behavior.

The approach simplifies analysis of large-scale traffic games.

Abstract

We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a particular route is charged a tax penalty that is affine in the logarithm of the number of agents selecting the same route. We show that the mean-field approximation of such a large-population dynamic game leads to the so-called linearly solvable Markov decision process, implying that an open-loop $\epsilon$-Nash equilibrium of the original game can be found simply by solving a finite-dimensional linear system.