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    On the convergence of finite state mean-field games through Γ-convergence

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    Type
    Article
    Authors
    Ferreira, Rita C.
    Gomes, Diogo A. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2014-10
    Permanent link to this record
    http://hdl.handle.net/10754/563769
    
    Metadata
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    Abstract
    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.
    Citation
    Ferreira, R., & Gomes, D. A. (2014). On the convergence of finite state mean-field games through Γ-convergence. Journal of Mathematical Analysis and Applications, 418(1), 211–230. doi:10.1016/j.jmaa.2014.02.044
    Sponsors
    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.
    Publisher
    Elsevier BV
    Journal
    Journal of Mathematical Analysis and Applications
    DOI
    10.1016/j.jmaa.2014.02.044
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jmaa.2014.02.044
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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