One-dimensional, forward-forward mean-field games with congestion

Handle URI:
http://hdl.handle.net/10754/626532
Title:
One-dimensional, forward-forward mean-field games with congestion
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Sedjro, Marc
Abstract:
Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of these games. First, by computing Riemann invariants and corresponding invariant regions, we develop a method to prove lower bounds for the density. Next, by combining the lower bound with an entropy function, we prove the existence of global solutions for parabolic forward-forward MFGs. Finally, we construct traveling-wave solutions, which settles in a negative way the convergence problem for forward-forward MFGs. A similar technique gives the existence of time-periodic solutions for non-monotonic MFGs.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
29-Mar-2017
ARXIV:
arXiv:1703.10029
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1703.10029v1; http://arxiv.org/pdf/1703.10029v1
Appears in Collections:
Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorSedjro, Marcen
dc.date.accessioned2017-12-28T07:32:15Z-
dc.date.available2017-12-28T07:32:15Z-
dc.date.issued2017-03-29en
dc.identifier.urihttp://hdl.handle.net/10754/626532-
dc.description.abstractHere, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of these games. First, by computing Riemann invariants and corresponding invariant regions, we develop a method to prove lower bounds for the density. Next, by combining the lower bound with an entropy function, we prove the existence of global solutions for parabolic forward-forward MFGs. Finally, we construct traveling-wave solutions, which settles in a negative way the convergence problem for forward-forward MFGs. A similar technique gives the existence of time-periodic solutions for non-monotonic MFGs.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1703.10029v1en
dc.relation.urlhttp://arxiv.org/pdf/1703.10029v1en
dc.rightsArchived with thanks to arXiven
dc.titleOne-dimensional, forward-forward mean-field games with congestionen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.identifier.arxividarXiv:1703.10029en
kaust.authorGomes, Diogo A.en
kaust.authorSedjro, Marcen
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