Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule
- Journal Article
In this article we prove the existence of classical solutions to a system of mean field games arising in the study of exhaustible resource production under market competition. Individual trajectories are modeled by a controlled diffusion process with jumps, which adds a nonlocal term to the PDE system. The assumptions on the Hamiltonian are sufficiently general to cover a large class of examples proposed in the literature on Bertrand and Cournot mean field games. Uniqueness also holds under a sufficient restriction on the structure of the Hamiltonian, which in practice amounts to a small upper bound on the substitutability of goods. Show more
Journal / seriesJournal des Mathematiques Pures et Appliquees
Pages / Article No.
SubjectMean field games of controls; Extended mean field games; Economic models; Bertrand competition; Cournot competition
MoreShow all metadata