First order mean field games - explicit solutions, perturbations and connection with classical mechanics

Handle URI:
http://hdl.handle.net/10754/624802
Title:
First order mean field games - explicit solutions, perturbations and connection with classical mechanics
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Nurbekyan, Levon; Prazeres, Mariana
Abstract:
We 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
6-Jan-2016
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorNurbekyan, Levonen
dc.contributor.authorPrazeres, Marianaen
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.en
dc.subjectSDEen
dc.titleFirst order mean field games - explicit solutions, perturbations and connection with classical mechanicsen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
kaust.authorGomes, Diogo A.en
kaust.authorNurbekyan, Levonen
kaust.authorPrazeres, Marianaen
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