Master equation for Cournot mean field games of control with absorption

P. Jameson Graber, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)816-909
Number of pages94
JournalJournal of Differential Equations
StatePublished - Jan 15 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Exhaustible resources
  • Mean field games


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