Abstract
MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L 2 stability of the Fokker–Planck equation are the main ingredients of the proof.
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References
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Gomes, D.A., Pimentel, E.A., Voskanyan, V. (2016). Non-local Mean-Field Games: Existence. In: Regularity Theory for Mean-Field Game Systems. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-38934-9_10
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DOI: https://doi.org/10.1007/978-3-319-38934-9_10
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Online ISBN: 978-3-319-38934-9
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