Show simple item record

dc.contributor.authorGomes, Diogo A.
dc.contributor.authorNurbekyan, Levon
dc.contributor.authorPrazeres, Mariana
dc.date.accessioned2017-06-08T06:32:27Z
dc.date.available2017-06-08T06:32:27Z
dc.date.issued2016-01-06
dc.identifier.urihttp://hdl.handle.net/10754/624802
dc.description.abstractWe present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
dc.subjectSDE
dc.titleFirst order mean field games - explicit solutions, perturbations and connection with classical mechanics
dc.typePoster
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.conference.dateJanuary 5-10, 2016
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
dc.conference.locationKAUST
kaust.personGomes, Diogo A.
kaust.personNurbekyan, Levon
kaust.personPrazeres, Mariana
refterms.dateFOA2018-06-13T14:56:52Z


Files in this item

This item appears in the following Collection(s)

Show simple item record