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.
Citation
Nojood Almayouf. Levon Nurbekyan. Giorgia Pagliar. Marco Piccirilli. Sagar Pratapsi. Mariana Prazeres. João Reis. André Rodrigues. Orlando Romero. Maria Sargsyan. Tommaso Seneci. Elena Bachini. Chuliang Song. Kengo Terai. Ryota Tomisaki. Hector Velasco-Perez. Vardan Voskanyan. Xianjin Yang. Andreia Chapouto. Rita Ferreira. Diogo Gomes. Daniela Jordão. David Evangelista. Avetik Karagulyan. Juan Monasterio. "Existence of positive solutions for an approximation of stationary mean-field games." Involve 10 (3) 473 - 493, 2017. https://doi.org/10.2140/involve.2017.10.473
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