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

P. Jameson Graber; Alain Bensoussan

doi:10.1007/s00245-016-9366-0

Author(s)

P. Jameson Graber
Alain Bensoussan

Detail(s)

Original language	English
Pages (from-to)	47-71
Journal / Publication	Applied Mathematics & Optimization
Volume	77
Issue number	1
Online published	17 Jun 2016
Publication status	Published - Feb 2018

Link(s)

DOI	DOI https://doi.org/10.1007/s00245-016-9366-0 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84975156985&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(b8d6cb47-761a-4c26-84a2-dae402074859).html

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.

Research Area(s)

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

Citation Format(s)

[ RIS ] [ BibTeX ]

Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. / Graber, P. Jameson; Bensoussan, Alain.
In: Applied Mathematics & Optimization, Vol. 77, No. 1, 02.2018, p. 47-71.

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

Graber, PJ & Bensoussan, A 2018, 'Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games', Applied Mathematics & Optimization, vol. 77, no. 1, pp. 47-71. https://doi.org/10.1007/s00245-016-9366-0

Graber, P. J., & Bensoussan, A. (2018). Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. Applied Mathematics & Optimization, 77(1), 47-71. https://doi.org/10.1007/s00245-016-9366-0

Graber PJ, Bensoussan A. Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. Applied Mathematics & Optimization. 2018 Feb;77(1):47-71. Epub 2016 Jun 17. doi: 10.1007/s00245-016-9366-0

Graber, P. Jameson ; Bensoussan, Alain. / Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. In: Applied Mathematics & Optimization. 2018 ; Vol. 77, No. 1. pp. 47-71.