TY - JOUR
T1 - On the convergence of finite state mean-field games through Γ-convergence
AU - Ferreira, Rita C.
AU - Gomes, Diogo A.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: R. 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.
PY - 2014/10
Y1 - 2014/10
N2 - In 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.
AB - In 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.
UR - http://hdl.handle.net/10754/563769
UR - https://linkinghub.elsevier.com/retrieve/pii/S0022247X14001735
UR - http://www.scopus.com/inward/record.url?scp=84899964905&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2014.02.044
DO - 10.1016/j.jmaa.2014.02.044
M3 - Article
SN - 0022-247X
VL - 418
SP - 211
EP - 230
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -