Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

P. Jameson Graber; Alain Bensoussan

doi:10.1007/s00245-016-9366-0

Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

P. Jameson Graber^*, Alain Bensoussan

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

27 Citations (Scopus)

Abstract

We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.

Original language	English
Pages (from-to)	47-71
Journal	Applied Mathematics & Optimization
Volume	77
Issue number	1
Online published	17 Jun 2016
DOIs	https://doi.org/10.1007/s00245-016-9366-0
Publication status	Published - Feb 2018

Research Keywords

Mean field games
Hamilton–Jacobi
Fokker–Planck
Coupled systems
Optimal control
Nonlinear partial differential equations

Access Output

10.1007/s00245-016-9366-0

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{b8d6cb47761a4c2684a2dae402074859,

title = "Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games",

abstract = "We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.",

keywords = "Mean field games, Hamilton–Jacobi, Fokker–Planck, Coupled systems, Optimal control, Nonlinear partial differential equations",

author = "Graber, {P. Jameson} and Alain Bensoussan",

year = "2018",

month = feb,

doi = "10.1007/s00245-016-9366-0",

language = "English",

volume = "77",

pages = "47--71",

journal = "Applied Mathematics & Optimization",

issn = "0095-4616",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

AU - Graber, P. Jameson

AU - Bensoussan, Alain

PY - 2018/2

Y1 - 2018/2

N2 - We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.

AB - We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a priori estimates, we prove the existence of classical solutions under general assumptions on the data. Moreover, under an additional hypothesis we prove uniqueness.

KW - Mean field games

KW - Hamilton–Jacobi

KW - Fokker–Planck

KW - Coupled systems

KW - Optimal control

KW - Nonlinear partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=84975156985&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84975156985&origin=recordpage

U2 - 10.1007/s00245-016-9366-0

DO - 10.1007/s00245-016-9366-0

M3 - RGC 21 - Publication in refereed journal

SN - 0095-4616

VL - 77

SP - 47

EP - 71

JO - Applied Mathematics & Optimization

JF - Applied Mathematics & Optimization

IS - 1

ER -

Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

GRF: Mean Field Theory, Stochastic Control and Systems of Partial Differential Equations

Cite this

Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Mean Field Theory, Stochastic Control and Systems of Partial Differential Equations

Cite this