Modeling and Computation of Differential Game and Mean Field Game

      This talk consists of two parts, one of which is about differential game for transboundary pollution. Here we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading, and derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The second part is concerned with the mean field game to model the production behaviors of a very large number of producers, and the Hamilton-Jacobi-Bellman equation coupled with a Kolmogorov equation are obtained. Then, the efficient fitted finite volume methods are proposed to solve the above systems of equations numerically.