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Two Numerical Approaches to Stationary Mean-Field Games

Author

Listed:
  • Noha Almulla

    (University of Dammam)

  • Rita Ferreira

    (King Abdullah University of Science and Technology (KAUST))

  • Diogo Gomes

    (King Abdullah University of Science and Technology (KAUST))

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.

Suggested Citation

  • Noha Almulla & Rita Ferreira & Diogo Gomes, 2017. "Two Numerical Approaches to Stationary Mean-Field Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 657-682, December.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0203-5
    DOI: 10.1007/s13235-016-0203-5
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    References listed on IDEAS

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    1. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
    2. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
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    Cited by:

    1. Piotr Więcek, 2020. "Discrete-Time Ergodic Mean-Field Games with Average Reward on Compact Spaces," Dynamic Games and Applications, Springer, vol. 10(1), pages 222-256, March.
    2. Diogo Aguiar Gomes & Ricardo de Lima Ribeiro, 2021. "Stationary mean-field games with logistic effects," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-34, February.
    3. Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.

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