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Pré-Publication, Document De Travail Année : 2024

A variational formulation of a Multi-Population Mean Field Games with non-local interactions

Résumé

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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Dates et versions

hal-04668323 , version 1 (06-08-2024)
hal-04668323 , version 2 (11-09-2024)

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  • HAL Id : hal-04668323 , version 1

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Luigi de Pascale, Luca Nenna. A variational formulation of a Multi-Population Mean Field Games with non-local interactions. 2024. ⟨hal-04668323v1⟩
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