Variational Methods for Mean Field Games with Degenerate Diffusion
Speaker: Jameson Graber, University of Texas, Dallas
Location: Warren Weaver Hall 1302
Date: Thursday, April 30, 2015, 11 a.m.
Mean field games have attracted lots of attention recently due to their applications in the social sciences and systems theory. In this study we develop a theory of existence and uniqueness a solutions to a coupled system of nonlinear PDEs describing mean field Nash equilibrium. It turns out that the system can be characterized as an optimality condition for the optimal control of the Fokker-Planck equation, where the adjoint state satisfies a Hamilton-Jacobi equation. Our variational methods are of particular interest when the PDEs are of degenerate parabolic type, for which traditional fixed-point methods break down due to lack of regularity.