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arXiv · 2007.10620

A quadratic Mean Field Games model for the Langevin equation

Fabio Camilli
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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 [9], 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.

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Fabio Camilli. 2020-07-21. A quadratic Mean Field Games model for the Langevin equation. https://arxiv.org/abs/2007.10620

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