Submitted:
10 January 2021
Posted:
12 January 2021
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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 [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
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