Back to Search
Start Over
Existence and uniqueness of solutions for Bertrand and Cournot mean field games
- Publication Year :
- 2015
-
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
- Subjects :
- Mathematics - Analysis of PDEs
FOS: Mathematics
35K61
Analysis of PDEs (math.AP)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2658ba2c204aa55403f1460b1d74f307