ABSTRACT

The theory of Mean Field Games was invented to study the limit of Nash equilibria of differential games when the number of players tends to infinity. It was introduced by J.-M. Lasry and P.-L. Lions, and independently by P. Caines, M. Huang and R. Malhame. A fundamental object in the theory is the so-called master equation, which fully characterizes the equilibria. This is an infinite dimensional nonlocal Hamilton-Jacobi equation on the space of probability measures endowed with the Monge-Kantorovich metric. A central question in the theory is the global well-posedness of this equation in various setting. In this talk, we will introduce our recent progress made on master equations on continuums and graphs. This is based on joint works with Wilfrid Gangbo(UCLA) and Jianfeng Zhang(USC).