MEAN FIELD GAMES EQUATIONS WITH QUADRATIC HAMILTONIAN: A SPECIFIC APPROACH

Source abstract

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to +∞, have been introduced by J.-M. Lasry and P.-L. Lions in Refs. 10–12. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in the case of a quadratic Hamiltonian. This system is then used to exhibit a monotonic scheme to build solutions of the MFG equations. Effective numerical methods based on this constructive scheme are presented and numerical experiments are carried out.