Two Numerical Approaches to Stationary Mean-Field Games

Abstract

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

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Correspondence to Diogo Gomes.

Additional information

The authors were partially supported by King Abdullah University of Science and Technology baseline and start-up funds and by KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering.

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Almulla, N., Ferreira, R. & Gomes, D. Two Numerical Approaches to Stationary Mean-Field Games. Dyn Games Appl 7, 657–682 (2017). https://doi.org/10.1007/s13235-016-0203-5

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Keywords

  • Mean-field games
  • Monotone schemes
  • Numerical methods