A weakly coupled mean field games model of first order for k groups of major players
Published in Proceedings of the American Mathematical Society, 2022
Recommended citation: P. Ni, K. Wang, and J. Yan, A weakly coupled mean field games model of first order for k groups of major players, Proc. Amer. Math. Soc., published online. https://www.ams.org/journals/proc/earlyview/#proc16342
The mean field games was introduced by J.-M. Lasry and P.-L. Lions and by P. E. Caines, M. Huang and R. P. Malhamé to analyze large population stochastic differential games. The first order mean field games system is a Hamilton-Jacobi equation coupled with a continuity equation. In this model, there is a large community of identical players. The cost functional of each player is determined by the same Hamiltonian. In most real problems of economics, there is not just one major player. So it is natural to consider a system with several major players. Different kinds of major players have different Hamiltonians. We introduced a weakly coupled mean field games model of first order for k different kinds of major players. We also proved the existence of weak solutions of this kind of weakly coupled mean field games model.
Recommended citation: P. Ni, K. Wang, and J. Yan, A weakly coupled mean field games model of first order for k groups of major players, Proc. Amer. Math. Soc., published online.