Almayouf, Nojood; Bachini, Elena; Chapouto, Andreia; Ferreira, Rita; Gomes, Diogo; Jordão, Daniela; Evangelista, David; Karagulyan, Avetik; Monasterio, Juan; Nurbekyan, Levon; Pagliar, Giorgia; Piccirilli, Marco; Pratapsi, Sagar; Prazeres, Mariana; Reis, João; Rodrigues, André; Romero, Orlando; Sargsyan, Maria; Seneci, Tommaso; Song, Chuliang; Terai, Kengo; Tomisaki, Ryota; Velasco-Perez, Hector; Voskanyan, Vardan; Yang, Xianjin Existence of positive solutions for an approximation of stationary mean-field games. (English) Zbl 1354.49082 Involve 10, No. 3, 473-493 (2017). Summary: 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. Cited in 2 Documents MSC: 49N70 Differential games and control 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 49M30 Other numerical methods in calculus of variations (MSC2010) 91A23 Differential games (aspects of game theory) 91A07 Games with infinitely many players 35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators Keywords:mean-field games; low-order regularizations; monotone methods; positive solutions PDFBibTeX XMLCite \textit{N. Almayouf} et al., Involve 10, No. 3, 473--493 (2017; Zbl 1354.49082) Full Text: DOI arXiv