Mean field game theory is the study of 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
master equation, which fully characterizes the limit equilibrium. In this
talk, we will introduce Mean field game and master equations on graphs. We will
construct solutions to both equations and link them to the solution to
a Hamilton-Jacobi equation on graph.