Hypoelliptic mean field games – a case study

Ermal Feleqi*, Diogo Gomes, Teruo Tada

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.

Original languageEnglish (US)
Pages (from-to)305-326
Number of pages22
JournalMinimax Theory and its Applications
Issue number2
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, Heldermann Verlag. All rights reserved.


  • Eigenvalue problems
  • Hypoelliptic operator
  • Mean-Field Games
  • Stationary problems

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization
  • Computational Mathematics


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