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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-04-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/2/68 |
| _version_ | 1797537208988598272 |
|---|---|
| author | Fabio Camilli |
| author_facet | Fabio Camilli |
| author_sort | Fabio Camilli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T12:12:51Z |
| format | Article |
| id | doaj.art-bb89bf02ebf741c599f7e3ce23353582 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T12:12:51Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-bb89bf02ebf741c599f7e3ce233535822023-11-21T16:07:59ZengMDPI AGAxioms2075-16802021-04-011026810.3390/axioms10020068A Quadratic Mean Field Games Model for the Langevin EquationFabio Camilli0Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via Scarpa 16, 00161 Roma, ItalyWe 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.https://www.mdpi.com/2075-1680/10/2/68langevin equationMean Field Games systemkinetic Fokker–Planck equationhypoelliptic operators |
| spellingShingle | Fabio Camilli A Quadratic Mean Field Games Model for the Langevin Equation Axioms langevin equation Mean Field Games system kinetic Fokker–Planck equation hypoelliptic operators |
| title | A Quadratic Mean Field Games Model for the Langevin Equation |
| title_full | A Quadratic Mean Field Games Model for the Langevin Equation |
| title_fullStr | A Quadratic Mean Field Games Model for the Langevin Equation |
| title_full_unstemmed | A Quadratic Mean Field Games Model for the Langevin Equation |
| title_short | A Quadratic Mean Field Games Model for the Langevin Equation |
| title_sort | quadratic mean field games model for the langevin equation |
| topic | langevin equation Mean Field Games system kinetic Fokker–Planck equation hypoelliptic operators |
| url | https://www.mdpi.com/2075-1680/10/2/68 |
| work_keys_str_mv | AT fabiocamilli aquadraticmeanfieldgamesmodelforthelangevinequation AT fabiocamilli quadraticmeanfieldgamesmodelforthelangevinequation |