# Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics

## TL;DR

This paper develops a mean-field game model for pedestrian crowds incorporating nonlocal crowd aversion, allowing for multiple interacting groups and capturing personal space preferences, with analysis and numerical simulations.

## Contribution

It introduces a novel mean-field type model with nonlocal crowd aversion and multiple groups, extending previous pedestrian crowd models.

## Key findings

- Model captures nonlocal crowd aversion behavior
- Derivation from particle system as mean-field game
- Numerical simulations illustrate pedestrian dynamics

## Abstract

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram (2011) to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a "personal space" where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type Maximum Principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.