Multi-population minimal-time mean field games

TL;DR

This paper studies a multi-population mean field game model where several groups aim to reach targets in minimal time, analyzing equilibria existence, behavior, and characterization without strong regularity assumptions.

Contribution

It introduces a new framework for multi-population mean field games focusing on minimal time objectives, establishing existence and characterization of equilibria under weak regularity conditions.

Findings

Existence of Lagrangian equilibria in multi-population mean field games.

Asymptotic behavior analysis of the equilibria.

Characterization of equilibria as solutions to a mean field game system.

Abstract

In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a control system depending on their position, the distribution of other agents in the same population, and the distribution of agents on other populations. Thus, interactions between agents occur through their dynamics. We consider in this paper the existence of Lagrangian equilibria to this mean field game, their asymptotic behavior, and their characterization as solutions of a mean field game system, under few regularity assumptions on agents' dynamics. In particular, the mean field game system is established without relying on semiconcavity properties of the value function.