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Existence of
positive solutions for an approximation of stationary
mean-field games
Nojood Almayouf, Elena Bachini, Andreia Chapouto, Rita Ferreira, Diogo Gomes, Daniela Jordão, David Evangelista Junior, Avetik Karagulyan, Juan Monasterio, Levon Nurbekyan, Giorgia Pagliar, Marco Piccirilli, Sagar Pratapsi, Mariana Prazeres, João Reis, André Rodrigues, Orlando Romero, Maria Sargsyan, Tommaso Seneci, Chuliang Song, Kengo Terai, Ryota Tomisaki, Hector Velasco-Perez, Vardan Voskanyan and Xianjin Yang |
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Vol. 10 (2017), No. 3, 473–493
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Abstract |
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Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a priori estimates with the continuation method. In contrast with high-order regularizations, the low-order regularizations are easier to implement numerically. Moreover, our methods give a theoretical foundation for this approach. |
Keywords
mean-field games, low-order regularizations, monotone
methods, positive solutions
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Mathematical Subject Classification 2010
Primary: 49L25, 91A13, 35J87
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Milestones
Received: 12 January 2016
Revised: 21 March 2016
Accepted: 15 April 2016
Published: 14 December 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Nojood Almayouf | |
| Effat University Jeddah 23523 Saudi Arabia |
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| Elena Bachini | |
| Department of Mathematics University of Padova I-35121 Padova Italy |
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| Andreia Chapouto | |
| University of Coimbra 5400-000 Chaves Portugal |
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| Rita Ferreira | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| Diogo Gomes | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| Daniela Jordão | |
| University of Coimbra 3001-501 Coimbra Portugal |
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| David Evangelista Junior | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| Avetik Karagulyan | |
| Faculty of Mathematics and
Mechanics Yerevan State University Republic of Armenia, Yerevan, 0025, 1 Alex Manoogian 0025 Yerevan Armenia |
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| Juan Monasterio | |
| University of Buenos Aires 1414CKS Buenos Aires Argentina |
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| Levon Nurbekyan | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| Giorgia Pagliar | |
| University of Verona I-37045 Legnago Italy |
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| Marco Piccirilli | |
| University of Rome Tor Vergata I-35121 Padova Italy |
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| Sagar Pratapsi | |
| University of Coimbra 4465-040 S. Mamede de Infesta Portugal |
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| Mariana Prazeres | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| João Reis | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| André Rodrigues | |
| University of Coimbra 3040-109 Coimbra Portugal |
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| Orlando Romero | |
| University of Lisbon 9000-690 Funchal Portugal |
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| Maria Sargsyan | |
| American University of Armenia 0025 Yerevan Armenia |
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| Tommaso Seneci | |
| University of Verona via Brunelleschi 1 I-37178 Verona Italy |
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| Chuliang Song | |
| MIT Cambridge, MA 02140 United States |
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| Kengo Terai | |
| Waseda University Saitama 338-0001 Japan |
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| Ryota Tomisaki | |
| Waseda University 210-10 Nase, Totsuka Yokohama 245-00051 Japan |
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| Hector Velasco-Perez | |
| National Autonomous University of
Mexico Cerro Copor #16 Campestre Churubusco 02100 Mexico City, Mexico |
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| Vardan Voskanyan | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| Xianjin Yang | |
| CEMSE Division King Abdullah University of Science and Technology (KAUST) Thuwal 23955-6900 Saudi Arabia |
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| © 2017 MSP (Mathematical Sciences Publishers). |
