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    Explicit Solutions for One-Dimensional Mean-Field Games

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    Type
    Thesis
    Authors
    Prazeres, Mariana cc
    Advisors
    Gomes, Diogo A. cc
    Committee members
    Markowich, Peter A. cc
    Sundaramoorthi, Ganesh cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2017-04-05
    Permanent link to this record
    http://hdl.handle.net/10754/623065
    
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    Abstract
    In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
    Citation
    Prazeres, M. (2017). Explicit Solutions for One-Dimensional Mean-Field Games. KAUST Research Repository. https://doi.org/10.25781/KAUST-34QJN
    DOI
    10.25781/KAUST-34QJN
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-34QJN
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; MS Theses; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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