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.
Highlights
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
We prove an existence result for the latter system, obtaining existence of a solution for the Mean Field Games system
The Mean Field Games (MFG in short) theory concerns the study of differential games with a large number of rational, indistinguishable agents and the characterization of the corresponding Nash equilibria
Summary
The Mean Field Games (MFG in short) theory concerns the study of differential games with a large number of rational, indistinguishable agents and the characterization of the corresponding Nash equilibria. 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.
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