# Linearly Solvable Mean-Field Traffic Routing Games

arXiv: https://arxiv.org/abs/1903.01449 · HTML: https://mlsanity.com/paper/1903.01449/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2019.

## Built on by (most cited first, 5 of 5)

- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Hypergraphon Mean Field Games](https://mlsanity.com/paper/2203.16223/) (2022)
- [Kernel Based Maximum Entropy Inverse Reinforcement Learning for Mean-Field Games](https://mlsanity.com/paper/2507.14529/) (2025)
- [A Constraint-Preserving Neural Network Approach for Solving Mean-Field Games Equilibrium](https://mlsanity.com/paper/2501.17450/) (2025)
- [Neural Parameter Calibration for Finite-State Mean Field Games](https://mlsanity.com/paper/2606.23155/) (2026)

## Abstract (arXiv)

We consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers selecting the same route. We show that the mean-field approximation of such a game leads to the so-called linearly solvable Markov decision process, implying that its mean-field equilibrium (MFE) can be found simply by solving a finite-dimensional linear system backward in time. Based on this backward-only characterization, it is further shown that the obtained MFE has the notable property of strong time-consistency. A connection between the obtained MFE and a particular class of fictitious play is also discussed.