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Human Crowds and Groups Interactions: a Mean Field Games Approach

Lachapelle, Aimé (2010), Human Crowds and Groups Interactions: a Mean Field Games Approach. https://basepub.dauphine.fr/handle/123456789/4275

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00484097/fr/
Date
2010
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
6
Metadata
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Author(s)
Lachapelle, Aimé
Abstract (EN)
This paper is devoted to some Mean Field Games (hereafter MFG) modeling of human crowds behavior. More precisely, we study 2-population dynamics (each of whom consisting of a continuum of individuals) with opposit interests. We focus on the crowd aversion case inside the group and also onto the other group (xenophobia in some cases). We write a macro-Nash problem between the two populations, then we give an existence and uniqueness result and characterize optimal points as MFG solutions. Finally we provide a simple gradient descent method to approximate the solutions and show some simulations.
Subjects / Keywords
Numerical approximations; Optimal control; Mean field games