Accepted Paper

Inserted: 6 aug 2024
Last Updated: 10 jul 2026

Journal: Nonlinear Differential Equations and Applications NoDEA.
Year: 2026

Abstract:

We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an Eulerian variational formulation which, despite the non convexity of the interaction, still gives a weak solution to the MFG model. The problem can be reformulated in Lagrangian terms and solved numerically by a Sinkhorn-like scheme. We present numerical results based on this approach, these simulations exhibit different behaviours depending on the nature (repulsive or attractive) of the non-local interaction.

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• A_variational_formulation_of_Multi_Population_Mean_Field_Games.pdf