- Alpar Meszaros
- Durham University, UK
- Date: Sept. 11, Wednesday, 2024
- Time: 11:00am -- 11:50am
- Host: Yuming Paul Zhang
- Room: Zoom: 84685608943 (Parker 328)
- 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 hyperbolic 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.