In this talk we address the study of long time convergence (trend to equilibrium problem) for finite state mean-field games using $\Gamma$-convergence. Our techniques are based upon the observation that an important class of mean-field games can be seen as the Euler-Lagrange equation of a suitable functional. Therefore, by a scaling argument, one can convert the long time convergence problem into a $\Gamma$-convergence problem. Our results generalize previous results on long-time convergence for finite state problems.
Rita Ferreira is a PostDoc Fellow at Instituto Superior Técnico of the University of Lisbon (IST-UL), a Visiting Assistant Professor at the Department of Mathematics of the Faculdade de Ciências e Tecnologia of the New University of Lisbon (FCT-UNL), and a Member of the Research Center of Mathematics and Applications of the FCT-UNL, Portugal. She received her BSc and a MSc in Mathematics at Faculty of Sciences of the University of Lisbon, Portugal, and her dual PhD degree in Mathematics at Carnegie Mellon University (CMU), USA, and at New University of Lisbon (UNL), Portugal, under the supervision of Prof. Irene Fonseca (CMU) and Prof. Luísa Mascarenhas (UNL). Her research interests lie in the areas of Partial Differential Equations, Continuum Mechanics, Calculus of Variations, and Homogenization. Her research activities have been focused on asymptotic analysis using variational methods of dimension reduction and homogenization problems. Currently, she is very interested in the mathematical study of problems in imaging processing and in mean-field games.