A Quadratic Mean Field Games Model for the Langevin Equation

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. An appropriate change of variables 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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