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dc.contributor.authorFerreira, Rita
dc.contributor.authorGomes, Diogo A.
dc.date.accessioned2019-02-20T07:20:01Z
dc.date.available2019-02-20T07:20:01Z
dc.date.issued2018-12-04
dc.identifier.citationFerreira R, Gomes D (2018) Existence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities. SIAM Journal on Mathematical Analysis 50: 5969–6006. Available: http://dx.doi.org/10.1137/16M1106705.
dc.identifier.issn0036-1410
dc.identifier.issn1095-7154
dc.identifier.doi10.1137/16M1106705
dc.identifier.urihttp://hdl.handle.net/10754/631098
dc.description.abstractHere, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions induced by monotonicity. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequality techniques, we prove the existence of solutions to the regularized problem. Then, using Minty's method, we establish the existence of weak solutions for the original MFG. Finally, we examine the properties of these weak solutions in several examples. Our methods provide a general framework to construct weak solutions to stationary MFGs with local, nonlocal, or congestion terms.
dc.description.sponsorshipThe work of the authors was partially supported by KAUST baseline and start-up funds and by KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/16M1106705
dc.rightsArchived with thanks to SIAM Journal on Mathematical Analysis
dc.subjectMean-field games
dc.subjectStationary problems
dc.subjectVariational inequalities
dc.titleExistence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalSIAM Journal on Mathematical Analysis
dc.eprint.versionPublisher's Version/PDF
dc.identifier.arxivid1512.05828
kaust.personFerreira, Rita
kaust.personGomes, Diogo A.
refterms.dateFOA2019-02-20T08:08:00Z
dc.date.published-online2018-12-04
dc.date.published-print2018-01


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