Monotone numerical methods for finite-state mean-field games

Handle URI:
http://hdl.handle.net/10754/626519
Title:
Monotone numerical methods for finite-state mean-field games
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Saude, Joao
Abstract:
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
29-Apr-2017
ARXIV:
arXiv:1705.00174
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1705.00174v1; http://arxiv.org/pdf/1705.00174v1
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.authorSaude, Joaoen
dc.date.accessioned2017-12-28T07:32:14Z-
dc.date.available2017-12-28T07:32:14Z-
dc.date.issued2017-04-29en
dc.identifier.urihttp://hdl.handle.net/10754/626519-
dc.description.abstractHere, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1705.00174v1en
dc.relation.urlhttp://arxiv.org/pdf/1705.00174v1en
dc.rightsArchived with thanks to arXiven
dc.titleMonotone numerical methods for finite-state mean-field gamesen
dc.typePreprinten
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionCarnegie Mellon University, Electrical and Computer Engineering department. 5000 Forbes Avenue Pittsburgh, PA 15213-3890 USA.en
dc.identifier.arxividarXiv:1705.00174en
kaust.authorGomes, Diogo A.en
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