# Mean field games with nonlinear mobilities in pedestrian dynamics

arXiv: https://arxiv.org/abs/1304.5201 · HTML: https://mlsanity.com/paper/1304.5201/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2013.

## Built on by (most cited first, 3 of 3)

- [Review of Pedestrian Trajectory Prediction Methods: Comparing Deep Learning and Knowledge-based Approaches](https://mlsanity.com/paper/2111.06740/) (2021)
- [Individual-Level Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2202.06401/) (2022)
- [Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation](https://mlsanity.com/paper/2408.08192/) (2024)

## Abstract (arXiv)

In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.