Speaker: Alpár R. Mészáros (Associate Professor, Durham University, UK)

Abstract: The theory of mean field games (MFG) was initiated around 2006 by two groups, Lasry-Lions and Huang-Malhamé-Caines. Their main goal was to characterize limits of Nash equilibria of N-player stochastic differential games, as the number of agents tends to infinity. In this talk we will present some recent progress in the theory, with a particular focus on the so-called master equation, proposed by Lions. This is a PDE of parabolic type set on the space of probability measures, which encapsulates all the information about the underlying games. We will be focusing on a class of data that fulfill the so-called displacement monotonicity condition — rooted in the theory of optimal transport — which ensures global well-posedness of the corresponding master equations.

 

 

Host: Yuming Paul Zhang