I will discuss the issue of existence of solutions to viscous Mean Field Games systems in the so-called anti-monotone regime, that describe Nash equilibria in differential games involving a large population of identical players aiming at aggregating. The problem can be recast into the optimal control of a system whose state is driven by a Fokker-Planck equation. I will show the role of the aggregation strength in the existence of equilibria, which may correspond to global or local minima of a suitable functional, or their nonexistence. The stationary and the evolutive case, which correspond to long-time and fixed time horizon optimization respectively, will be discussed and compared.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
