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    On the Existence of Solutions for Stationary Mean-Field Games with Congestion

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    mfg_stationary_congestion_revised.pdf
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    Type
    Article
    Authors
    Evangelista, David cc
    Gomes, Diogo A. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-09-11
    Preprint Posting Date
    2016-11-24
    Online Publication Date
    2017-09-11
    Print Publication Date
    2018-12
    Permanent link to this record
    http://hdl.handle.net/10754/625765
    
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    Abstract
    Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.
    Citation
    Evangelista D, Gomes DA (2017) On the Existence of Solutions for Stationary Mean-Field Games with Congestion. Journal of Dynamics and Differential Equations. Available: http://dx.doi.org/10.1007/s10884-017-9615-1.
    Sponsors
    D. Gomes and D. Evangelista were partially supported baseline and start-up funds from King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Journal of Dynamics and Differential Equations
    DOI
    10.1007/s10884-017-9615-1
    arXiv
    1611.08232
    Additional Links
    http://link.springer.com/article/10.1007/s10884-017-9615-1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10884-017-9615-1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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