On the Existence of Solutions for Stationary Mean-Field Games with Congestion

Handle URI:
http://hdl.handle.net/10754/625765
Title:
On the Existence of Solutions for Stationary Mean-Field Games with Congestion
Authors:
Evangelista, David; Gomes, Diogo A. ( 0000-0002-3129-3956 )
Abstract:
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Evangelista D, Gomes DA (2017) On the Existence of Solutions for Stationary Mean-Field Games with Congestion. Journal of Dynamics and Differential Equations. Available: http://dx.doi.org/10.1007/s10884-017-9615-1.
Publisher:
Springer Nature
Journal:
Journal of Dynamics and Differential Equations
Issue Date:
11-Sep-2017
DOI:
10.1007/s10884-017-9615-1
Type:
Article
ISSN:
1040-7294; 1572-9222
Sponsors:
D. Gomes and D. Evangelista were partially supported baseline and start-up funds from King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://link.springer.com/article/10.1007/s10884-017-9615-1
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorEvangelista, Daviden
dc.contributor.authorGomes, Diogo A.en
dc.date.accessioned2017-10-03T12:49:38Z-
dc.date.available2017-10-03T12:49:38Z-
dc.date.issued2017-09-11en
dc.identifier.citationEvangelista D, Gomes DA (2017) On the Existence of Solutions for Stationary Mean-Field Games with Congestion. Journal of Dynamics and Differential Equations. Available: http://dx.doi.org/10.1007/s10884-017-9615-1.en
dc.identifier.issn1040-7294en
dc.identifier.issn1572-9222en
dc.identifier.doi10.1007/s10884-017-9615-1en
dc.identifier.urihttp://hdl.handle.net/10754/625765-
dc.description.abstractMean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.en
dc.description.sponsorshipD. Gomes and D. Evangelista were partially supported baseline and start-up funds from King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s10884-017-9615-1en
dc.subjectMean-field gamesen
dc.subjectCongestion problemsen
dc.subjectStationary problemsen
dc.titleOn the Existence of Solutions for Stationary Mean-Field Games with Congestionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Dynamics and Differential Equationsen
kaust.authorEvangelista, Daviden
kaust.authorGomes, Diogo A.en
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