Some results on the long time behavior of equilibria in MFG

Mer, 16/02/2022 - 10:30 / 11:30

405, Viale Romania

Speaker: Marco Cirant , Università degli Studi di Padova

Abstract

The theory of Mean Field Games is devoted to the study of Nash equilibria in (differential) games involving a population of infinitely many identical players. In the PDE framework, a MFG system consists of coupled Hamilton-Jacobi and Fokker-Planck equations, which characterize the equilibria of the population. I will discuss in the talk some results on the long time behaviour of solutions. First, I will show some models where aggregation among players is strongly encouraged that exhibit periodic in time solutions. Then, I will show that long time stability, namely the convergence to stationary equilibria can be proven if the aggregation effect is mild enough.