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; Xianjin Yang

doi:10.2140/involve.2017.10.473

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 SongKengo Terai, Ryota Tomisaki, Hector Velasco-Perez, Vardan Voskanyan, Xianjin Yang

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	473-493
Number of pages	21
Journal	Involve
Volume	10
Issue number	3
DOIs	https://doi.org/10.2140/involve.2017.10.473
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017, Mathematical Sciences Publishers. All rights reserved.

Keywords

low-order regularizations
mean-field games
monotone methods
positive solutions

ASJC Scopus subject areas

General Mathematics

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10.2140/involve.2017.10.473

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Almayouf, N., Bachini, E., Chapouto, A., Ferreira, R., Gomes, D., Jordão, D., Evangelista Junior, D., Karagulyan, A., Monasterio, J., Nurbekyan, L., Pagliar, G., Piccirilli, M., Pratapsi, S., Prazeres, M., Reis, J., Rodrigues, A., Romero, O., Sargsyan, M., Seneci, T., ... Yang, X. (2017). Existence of positive solutions for an approximation of stationary mean-field games. Involve, 10(3), 473-493. https://doi.org/10.2140/involve.2017.10.473

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abstract = "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.",

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Almayouf, N, Bachini, E, Chapouto, A, Ferreira, R , Gomes, D, Jordão, D, Evangelista Junior, D, Karagulyan, A, Monasterio, J, Nurbekyan, L, Pagliar, G, Piccirilli, M, Pratapsi, S, Prazeres, M, Reis, J, Rodrigues, A, Romero, O, Sargsyan, M, Seneci, T, Song, C, Terai, K, Tomisaki, R, Velasco-Perez, H, Voskanyan, V & Yang, X 2017, 'Existence of positive solutions for an approximation of stationary mean-field games', Involve, vol. 10, no. 3, pp. 473-493. https://doi.org/10.2140/involve.2017.10.473

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T1 - Existence of positive solutions for an approximation of stationary mean-field games

AU - Almayouf, Nojood

AU - Bachini, Elena

AU - Chapouto, Andreia

AU - Ferreira, Rita

AU - Gomes, Diogo

AU - Jordão, Daniela

AU - Evangelista Junior, David

AU - Karagulyan, Avetik

AU - Monasterio, Juan

AU - Nurbekyan, Levon

AU - Pagliar, Giorgia

AU - Piccirilli, Marco

AU - Pratapsi, Sagar

AU - Prazeres, Mariana

AU - Reis, João

AU - Rodrigues, André

AU - Romero, Orlando

AU - Sargsyan, Maria

AU - Seneci, Tommaso

AU - Song, Chuliang

AU - Terai, Kengo

AU - Tomisaki, Ryota

AU - Velasco-Perez, Hector

AU - Voskanyan, Vardan

AU - Yang, Xianjin

PY - 2017

Y1 - 2017

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KW - mean-field games

KW - monotone methods

KW - positive solutions

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Existence of positive solutions for an approximation of stationary mean-field games

Abstract

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Keywords

ASJC Scopus subject areas

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