Particle approximation of one-dimensional Mean-Field-Games with local interactions-Reference-Cited by-同舟云学术

Particle approximation of one-dimensional Mean-Field-Games with local interactions

Published:2022 Issue:7 Volume:42 Page:3569
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Francesco Marco Di¹,Duisembay Serikbolsyn²,Gomes Diogo Aguiar²,Ribeiro Ricardo²

Affiliation:

1. University of L'Aquila, Department of Information Engineering, Computer Science, and Mathematics (DISIM), Via Vetoio 1, Coppito, I-67100 L'Aquila, Italy

2. King 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

Abstract

<p style='text-indent:20px;'>We 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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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