On the convergence of finite state mean-field games through Γ-convergence
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractIn this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
SponsorsR. Ferreira was supported partially by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through grants SFRH/BPD/81442/2011 and PEst-OE/MAT/UIO297/2011 (CMA).Comes was supported partially by CAMGSD-LARSys through FCT and by grants PTDC/MAT-CAL/0749/2012, UTACMU/MAT/0007/2009, PTDC/MAT/114397/2009, and UTAustin/MAT/0057/2008.