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dc.contributor.authorEvangelista, David
dc.contributor.authorFerreira, Rita
dc.contributor.authorGomes, Diogo A.
dc.contributor.authorNurbekyan, Levon
dc.contributor.authorVoskanyan, Vardan K.
dc.date.accessioned2018-05-06T14:23:56Z
dc.date.available2018-01-15T13:25:51Z
dc.date.available2018-05-06T14:23:56Z
dc.date.issued2018-04-30
dc.identifier.citationEvangelista D, Ferreira R, Gomes DA, Nurbekyan L, Voskanyan V (2018) First-order, stationary mean-field games with congestion. Nonlinear Analysis 173: 37–74. Available: http://dx.doi.org/10.1016/j.na.2018.03.011.
dc.identifier.issn0362-546X
dc.identifier.doi10.1016/j.na.2018.03.011
dc.identifier.urihttp://hdl.handle.net/10754/626821
dc.description.abstractMean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
dc.description.sponsorshipThe authors were partially supported by King Abdullah University of Science and Technology (KAUST) baseline and start-up funds, and grant OSR-CRG2017-3452.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/abs/1710.01566v1
dc.relation.urlhttp://arxiv.org/pdf/1710.01566v1
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0362546X18300695
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis, [173, , (2018-04-30)] DOI: 10.1016/j.na.2018.03.011 . © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCalculus of variations
dc.subjectCongestion
dc.subjectMean-field game
dc.titleFirst-order, stationary mean-field games with congestion
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalNonlinear Analysis
dc.eprint.versionPost-print
dc.identifier.arxividarXiv:1710.01566
kaust.personEvangelista da Silveira Junior, David
kaust.personFerreira, Rita
kaust.personGomes, Diogo A.
kaust.personNurbekyan, Levon
kaust.personVoskanyan, Vardan K.
kaust.grant.numberOSR-CRG2017-3452
dc.versionv1
dc.date.published-online2018-04-30
dc.date.published-print2018-08
dc.date.posted2017-10-04


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