Multi-population minimal-time mean field games

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.

References in corpus (1)

• Mean Field Games with state constraints: from mild to pointwise solutions of the PDE system

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• A note on existence and asymptotic behavior of Lagrangian equilibria for first-order optimal-exit mean field games