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

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Original languageEnglish
Pages (from-to)47-71
Journal / PublicationApplied Mathematics & Optimization
Issue number1
Online published17 Jun 2016
Publication statusPublished - Feb 2018


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