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.
A quadratic mean field games model for the langevin equation / Camilli, F.. - In: AXIOMS. - ISSN 2075-1680. - 10:2(2021). [10.3390/axioms10020068]
A quadratic mean field games model for the langevin equation
Camilli F.
2021
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. 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.File allegati a questo prodotto
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