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
TypeDocument de travail / Working paper
External document linkhttp://hal.archives-ouvertes.fr/hal-00484097/fr/
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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 / KeywordsNumerical approximations; Optimal control; Mean field games
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