Mean-field games with logistic population dynamics

Handle URI:
http://hdl.handle.net/10754/564832
Title:
Mean-field games with logistic population dynamics
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; De Lima Ribeiro, Ricardo
Abstract:
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
52nd IEEE Conference on Decision and Control
Conference/Event name:
52nd IEEE Conference on Decision and Control, CDC 2013
Issue Date:
Dec-2013
DOI:
10.1109/CDC.2013.6760258
Type:
Conference Paper
ISSN:
01912216
ISBN:
9781467357173
Appears in Collections:
Conference Papers; 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.authorDe Lima Ribeiro, Ricardoen
dc.date.accessioned2015-08-04T07:17:42Zen
dc.date.available2015-08-04T07:17:42Zen
dc.date.issued2013-12en
dc.identifier.isbn9781467357173en
dc.identifier.issn01912216en
dc.identifier.doi10.1109/CDC.2013.6760258en
dc.identifier.urihttp://hdl.handle.net/10754/564832en
dc.description.abstractIn its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleMean-field games with logistic population dynamicsen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journal52nd IEEE Conference on Decision and Controlen
dc.conference.date10 December 2013 through 13 December 2013en
dc.conference.name52nd IEEE Conference on Decision and Control, CDC 2013en
dc.conference.locationFlorenceen
dc.contributor.institutionDepartamento de Mateḿatica, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, 1049-001 Lisboa, Portugalen
dc.contributor.institutionDepartamento de Mateḿatica Aplicada, Ministry of Education of Brazil, IME - USP and CAPES Foundation, Brasília DF 70040-020, Brazilen
kaust.authorGomes, Diogo A.en
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