Linearly-Solvable Mean-Field Approximation for Multi-Team Road Traffic Games

TL;DR

This paper introduces a mean-field approximation approach to analyze multi-team traffic routing games, enabling efficient computation of Nash equilibria in large populations with dynamic tax incentives.

Contribution

It presents a novel linear solvability framework for mean-field approximations in multi-team traffic games with logarithmic tax penalties.

Findings

Nash equilibrium can be efficiently computed using linear algorithms.

The model effectively mitigates congestion through dynamic taxes.

The approach scales to large populations with multiple teams.

Abstract

We study the traffic routing game among a large number of selfish drivers over a traffic network. We consider a specific scenario where the strategic drivers can be classified into teams, where drivers in the same team have identical payoff functions. An incentive mechanism is considered to mitigate congestion, where each driver is subject to dynamic tax penalties. We explore a special case in which the tax is affine in the logarithm of the number of drivers selecting the same route from each team. It is shown via a mean-field approximation that a Nash equilibrium in the limit of a large population can be found by linearly solvable algorithms.