Hybrid seminar at McGill University or Zoom.

The theory of Mean Field Games (MFGs) represents the most influential contribution to the rapid development of the study of differential games with many players in the last two decades. It provides an effective paradigm to deal with players interacting in such a way that they are indistinguishable, and individually negligible in the large population limit. In the last years, we have witnessed an increasing interest in the understanding of large population limits of Nash equilibria — or particle systems, in general — under more general assumptions on the interactions. On the one hand, if they are governed by dense graphs, then Graphon MF(G) theory helps to describe effectively such limits; on the other, as of today, less is known about sparse interactions. I will discuss some recent results on this last topic, mainly obtained in collaboration with Marco Cirant (Padova), showing how Nash equilibria of games with sparse interactions can be described — in the large population limit — by infinite-dimensional systems of Hamilton-Jacobi-Bellman equations, and giving insights on how such systems can be dealt with.

Bio: Davide Francesco Redaelli is post-doc research associate in mathematics at the University of Rome Tor Vergata. He received a MSc in Mathematics at the University of Milan, under the supervision of Prof. Kevin R. Payne, working on general potential theories for fully nonlinear PDEs, and a PhD in Mathematics at the University of Padua, under the supervision of Prof. Marco Cirant, working on nonlinear systems of PDEs arising in the theory of differential games.