Abstract
The paper studies the convergence, as N tends to infinity, of a system of N weakly coupled Hamilton–Jacobi equations (the open loop Nash system) when the coupling between the players becomes increasingly singular. The limit equation is a mean field game system with local coupling.
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Acknowledgements
The author thanks the anonymous referee for his/her comments which helped to improve the paper. The author was partially supported by the ANR (Agence Nationale de la Recherche) project ANR-16-CE40-0015-01. This work was also supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.
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Cardaliaguet, P. (2019). On the Convergence of Open Loop Nash Equilibria in Mean Field Games with a Local Coupling. In: Alabau-Boussouira, F., Ancona, F., Porretta, A., Sinestrari, C. (eds) Trends in Control Theory and Partial Differential Equations. Springer INdAM Series, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-17949-6_6
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