Master equation for Cournot mean field games of control with absorption

TY - JOUR

T1 - Master equation for Cournot mean field games of control with absorption

AU - Graber, P. Jameson

AU - Sircar, Ronnie

N1 - Publisher Copyright: © 2022 Elsevier Inc.

PY - 2023/1/15

Y1 - 2023/1/15

N2 - We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot competition between producers. The proof relies on an analysis of a forward-backward system of nonlocal Hamilton-Jacobi/Fokker-Planck equations with Dirichlet boundary conditions. In particular, we establish new a priori estimates to prove that solutions are differentiable with respect to the initial measure.

AB - We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot competition between producers. The proof relies on an analysis of a forward-backward system of nonlocal Hamilton-Jacobi/Fokker-Planck equations with Dirichlet boundary conditions. In particular, we establish new a priori estimates to prove that solutions are differentiable with respect to the initial measure.

KW - Exhaustible resources

KW - Mean field games

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U2 - 10.1016/j.jde.2022.10.031

DO - 10.1016/j.jde.2022.10.031

M3 - Article

SN - 0022-0396

VL - 343

SP - 816

EP - 909

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -