# Multi-population minimal-time mean field games

2 DISCO - Dynamical Interconnected Systems in COmplex Environments
Inria Saclay - Ile de France, L2S - Laboratoire des signaux et systèmes
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.
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https://hal.archives-ouvertes.fr/hal-03178357
Contributor : Guilherme Mazanti Connect in order to contact the contributor
Submitted on : Tuesday, December 7, 2021 - 11:42:22 AM
Last modification on : Friday, January 21, 2022 - 3:12:20 AM

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### Identifiers

• HAL Id : hal-03178357, version 2
• ARXIV : 2103.12668

### Citation

Saeed Sadeghi, Guilherme Mazanti. Multi-population minimal-time mean field games. 2021. ⟨hal-03178357v2⟩

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