The Convergence Problem in Mean Field Games with Neumann Boundary Conditions

Michele Ricciardi

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we study the convergence of Nash equilibria in an N-player differential game towards the optimal strategies in the mean field games when the dynamic of the generic player includes a reflection process which guarantees the invariance of the state space \Omega . The well-posedness of the master equation allows us to use its solution U in order to construct finite-dimensional projections uNi, which will satisfy | uNi - vNi| \rightarrow 0 forN\rightarrow +\infty almost surely, where (vNi)iis the solution of the Nash system.
Original languageEnglish (US)
Pages (from-to)3316-3343
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume55
Issue number4
DOIs
StatePublished - Aug 2 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-08-07
Acknowledgements: I wish to sincerely thank P. Cardaliaguet and A. Porretta for their help and support during the preparation of this article. I wish to thank also F. Delarue for sharing his enlightening.

ASJC Scopus subject areas

  • Computational Mathematics
  • Analysis
  • Applied Mathematics

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