Continuous time finite state mean field games

Handle URI:
http://hdl.handle.net/10754/562726
Title:
Continuous time finite state mean field games
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Mohr, Joana; Souza, Rafael Rigão
Abstract:
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Springer Verlag
Journal:
Applied Mathematics and Optimization
Issue Date:
23-Apr-2013
DOI:
10.1007/s00245-013-9202-8
Type:
Article
ISSN:
00954616
Sponsors:
D. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT-CAL/0749/2012, UTA-CMU/MAT/0007/2009 PTDC/MAT/114397/2009, UTAustin-MAT/0057/2008, and by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. R.R.S. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. J.M. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorMohr, Joanaen
dc.contributor.authorSouza, Rafael Rigãoen
dc.date.accessioned2015-08-03T11:03:24Zen
dc.date.available2015-08-03T11:03:24Zen
dc.date.issued2013-04-23en
dc.identifier.issn00954616en
dc.identifier.doi10.1007/s00245-013-9202-8en
dc.identifier.urihttp://hdl.handle.net/10754/562726en
dc.description.abstractIn this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.en
dc.description.sponsorshipD. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT-CAL/0749/2012, UTA-CMU/MAT/0007/2009 PTDC/MAT/114397/2009, UTAustin-MAT/0057/2008, and by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. R.R.S. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09. J.M. was partially supported by the bilateral agreement Brazil-Portugal (CAPES-FCT) 248/09.en
dc.publisherSpringer Verlagen
dc.titleContinuous time finite state mean field gamesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalApplied Mathematics and Optimizationen
dc.contributor.institutionCenter for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugalen
dc.contributor.institutionInstituto de Matemática, UFRGS, 91509-900 Porto Alegre, Brazilen
kaust.authorGomes, Diogo A.en
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