Particle approximation of one-dimensional Mean-Field-Games with local interactions
KAUST DepartmentKing Abdullah University of Science and Technology (KAUST), CEMSE Division, KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering, Thuwal 23955-6900, Saudi Arabia
Applied Mathematics & Computational Sci
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberOSR-CRG2021-4674
Permanent link to this recordhttp://hdl.handle.net/10754/671167
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AbstractWe study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As we deal with the planning problem, we prescribe initial and terminal distributions for the transport equation. The particle approximation builds on a semi-discrete variational problem. First, we address the existence and uniqueness of a solution to the semi-discrete variational problem. Next, we show that our discretization preserves some previously identified conserved quantities. Finally, we prove that the approximation by particle systems preserves displacement convexity. We use this last property to establish uniform estimates for the discrete problem. We illustrate our results for the discrete problem with numerical examples.
CitationFrancesco, M. D., Duisembay, S., Gomes, D. A., & Ribeiro, R. (2022). Particle approximation of one-dimensional Mean-Field-Games with local interactions. Discrete & Continuous Dynamical Systems, 0(0), 0. https://doi.org/10.3934/dcds.2022025
SponsorsM. Di Francesco was supported by KAUST during his visit in 2020. S. Duisembay, D. A. Gomes and R. Ribeiro were partially supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2021-4674.