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    Socio-economic applications of finite state mean field games

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    Type
    Article
    Authors
    Gomes, Diogo A. cc
    Machado Velho, Roberto
    Wolfram, Marie Therese
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-10-06
    Online Publication Date
    2014-10-06
    Print Publication Date
    2014-10-06
    Permanent link to this record
    http://hdl.handle.net/10754/594151
    
    Metadata
    Show full item record
    Abstract
    In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
    Citation
    Gomes D, Velho RM, Wolfram M-T (2014) Socio-economic applications of finite state mean field games. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372: 20130405–20130405. Available: http://dx.doi.org/10.1098/rsta.2013.0405.
    Sponsors
    D. G. was partially supported by KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering and CAMGSD-LARSys (FCT-Portugal), PTDC/MAT-CAL/0749/2012 (FCT-Portugal). R. M. V. was partially supported by CNPq-Brazil through a PhD scholarship 'Programme Science without Borders and KAUST' Saudi Arabia. M.-T.W. acknowledges support from the Austrian Academy of Sciences OAW via the New Frontiers Project NST-001.
    Publisher
    The Royal Society
    Journal
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
    DOI
    10.1098/rsta.2013.0405
    PubMed ID
    25288816
    arXiv
    1403.4217
    ae974a485f413a2113503eed53cd6c53
    10.1098/rsta.2013.0405
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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