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arXiv · 1511.06999

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
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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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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. 2015-12-14. Existence of positive solutions for an approximation of stationary mean-field games. https://doi.org/10.2140/involve.2017.10.473

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