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

References in corpus (3)

• Weak solutions for mean field games with congestion
• Existence for stationary mean field games with quadratic Hamiltonians with congestion
• On a Boltzmann mean field model for knowledge growth

Cited by in corpus (1)

• Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource