A variational formulation of a Multi-Population Mean Field Games with non-local interactions
<|reference_start|>A variational formulation of a Multi-Population Mean Field Games with non-local interactions: 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.<|reference_end|>
@article{de pascale2024a,
    title={A variational formulation of a Multi-Population Mean Field Games with
  non-local interactions},
    author={Luigi De Pascale and Luca Nenna},
    journal={arXiv preprint arXiv:2408.03118},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03118},
    primaryClass={math.AP cs.NA math.NA math.OC}
}