Mass concentration for Ergodic Mean-Field Games with Riesz-type aggregation
speaker: Chiara Bernardini (Università degli Studi di Padova)abstract: We consider second-order ergodic Mean-Field Games systems defined in the whole space R N with Riesz-type aggregating nonlocal coupling and external confining potential V . In this setting, every player of the game is attracted toward regions where the population is highly distributed, while the external potential discourages agents to be far away from the origin. Focusing on the mass-subcritical regime N − γ
0 < α < N, we show concentration phenomena in the vanishing viscosity limit, namely when the diffusion becomes negligible. First, we investigate the asymptotic behavior of rescaled solutions as ε → 0, obtaining in this way existence of classical solutions to potential-free MFG systems with Riesz-type coupling. Secondly, we prove concentration of mass around minima of the potential V .
timetable:
Mon 8 May, 16:30 - 17:00, Aula Dini
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