Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition

Diogo A. Gomes*, João Saúde

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions make the numerical approximation of MFGs difficult. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve both for stationary and time-dependent MFGs. We illustrate our methods with a MFG that models the paradigm-shift problem.

Original languageEnglish (US)
Pages (from-to)51-82
Number of pages32
JournalApplied Mathematics and Optimization
Issue number1
StatePublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Finite state problems
  • Mean-field games
  • Monotonicity methods

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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