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Two Numerical Approaches to Stationary Mean-Field Games

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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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Author information

Authors and Affiliations

  1. College of Science, University of Dammam, King Faisal Road, Dammam, Saudi Arabia

    Noha Almulla

  2. CEMSE Division and KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia

    Rita Ferreira & Diogo Gomes

Authors
  1. Noha Almulla
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  2. Rita Ferreira
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  3. Diogo Gomes
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Corresponding author

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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