Mean field games equations with quadratic Hamiltonian: a specific approach
For researchers in stochastic differential games and PDEs, this provides a new constructive approach for a specific class of MFG equations, though it is incremental as it relies on a known transformation.
The authors transform mean field games equations with a quadratic Hamiltonian into a simpler system of PDEs, enabling a monotonic scheme for constructing solutions and effective numerical methods with experiments.
Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. 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.