Résumé en anglais

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.