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Human Crowds and Groups Interactions: a Mean Field Games Approach

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Date
2010
Publisher city
Paris
Publisher
Université Paris-Dauphine
Link to item file
http://hal.archives-ouvertes.fr/hal-00484097/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
Numerical approximations; Optimal control; Mean field games
URI
https://basepub.dauphine.fr/handle/123456789/4275
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Lachapelle, Aimé
Type
Document de travail / Working paper
Item number of pages
6
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.

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SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

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