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A Quadratic Mean Field Games Model for the Langevin Equation
Version 1
: Received: 10 January 2021 / Approved: 12 January 2021 / Online: 12 January 2021 (09:31:54 CET)
A peer-reviewed article of this Preprint also exists.
Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Axioms 2021, 10, 68. Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Axioms 2021, 10, 68.
Journal reference: Axioms 2021, 10, 68
DOI: 10.3390/axioms10020068
Abstract
We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.
Keywords
Langevin equation; Mean Field Games system; kinetic Fokker-Planck equation
Subject
MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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