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dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorPrazeres, Mariana
dc.date.accessioned2017-04-06T05:42:41Z
dc.date.available2017-04-06T05:42:41Z
dc.date.issued2017-04-05
dc.identifier.citationPrazeres, M. (2017). Explicit Solutions for One-Dimensional Mean-Field Games. KAUST Research Repository. https://doi.org/10.25781/KAUST-34QJN
dc.identifier.doi10.25781/KAUST-34QJN
dc.identifier.urihttp://hdl.handle.net/10754/623065
dc.description.abstractIn 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.
dc.language.isoen
dc.subjectPDE's
dc.subjectexplicit solutions
dc.subjectMean-field games
dc.titleExplicit Solutions for One-Dimensional Mean-Field Games
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberMarkowich, Peter A.
dc.contributor.committeememberSundaramoorthi, Ganesh
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-14T05:03:30Z


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