Mean Field Games Systems

Prof. Dr. Alessio Porretta (Università degli Studi di Roma "Tor Vergata")

25 October 2016, 10:15 - 12:00, HG G 19.2
01 November 2016, 10:15 - 12:00, HG G 19.2

Abstract

Mean field games theory has been developed since 2006 by J.-M. Lasry and P.-L. Lions as amodel to describe Nash equilibria in the dynamic optimization of a large population of similar agents, where the individual strategy depends on the collective behavior through the distribution law of the states. This model leads to systems of PDEs where a backward Hamilton-Jacobi-Bellman equation is coupled with a  forward Kolmogorov equation.

In this course, after a brief description of the model we will present the main features of those PDE systems, discussing the existence, uniqueness and stability of solutions as well as further questions possibly related to optimal transport and control theory.