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 re...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/2/68 |
| Summary: | 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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| ISSN: | 2075-1680 |