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
December 2016
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.
Publication
Involve, a Journal of Mathematics

PostDoc
I am a quantitative ecologist driven by the curiosity of how biodiversity is generated and maintained.