Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Axioms2021, 10, 68.
Camilli, F. A Quadratic Mean Field Games Model for the Langevin Equation. Axioms 2021, 10, 68.
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 , 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.
Langevin equation; Mean Field Games system; kinetic Fokker-Planck equation
MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory
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