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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.

Authors:
;  [1]
  1. The University of Texas at Dallas, International Center for Decision and Risk Analysis, Naveen Jindal School of Management (United States)
Publication Date:
OSTI Identifier:
22756223
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 77; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; Article Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FOKKER-PLANCK EQUATION; HAMILTON-JACOBI EQUATIONS; MATHEMATICAL SOLUTIONS; MEAN-FIELD THEORY; OPTIMAL CONTROL

Citation Formats

Graber, P. Jameson, E-mail: pjg140130@utdallas.edu, and Bensoussan, Alain. Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. United States: N. p., 2018. Web. doi:10.1007/S00245-016-9366-0.
Graber, P. Jameson, E-mail: pjg140130@utdallas.edu, & Bensoussan, Alain. Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games. United States. doi:10.1007/S00245-016-9366-0.
Graber, P. Jameson, E-mail: pjg140130@utdallas.edu, and Bensoussan, Alain. Thu . "Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games". United States. doi:10.1007/S00245-016-9366-0.
@article{osti_22756223,
title = {Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games},
author = {Graber, P. Jameson, E-mail: pjg140130@utdallas.edu and Bensoussan, Alain},
abstractNote = {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.},
doi = {10.1007/S00245-016-9366-0},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 1,
volume = 77,
place = {United States},
year = {2018},
month = {2}
}