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A note on first order quasi-stationary Mean Field Games

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arxiv 2409.18483 v1 pith:I4HQXTQZ submitted 2024-09-27 math.OC

Fabio Camilli , Claudio Marchi , Cristian Mendico This is my paper · ORCID
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keywords fieldgamesmeanquasi-stationaryassumptionscontinuityequationaddress
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Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-order quasi-stationary Mean Field Games system, which involves an ergodic Hamilton-Jacobi equation and an evolutive continuity equation. Our approach relies on weak KAM theory. We introduce assumptions on the Hamiltonian and coupling cost to ensure continuity of the Peierls barrier and the Aubry set over time. These assumptions, though restrictive, cover interesting cases such as perturbed mechanical Hamiltonians.

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  1. Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games

    math.AP 2025-07 conditional novelty 7.0 of 10

    Existence and a vanishing-discount selection criterion are proved for quasi-stationary first-order contact mean-field games, with the selected limit given by Peierls barriers.

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