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

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Abstract

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.

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Authors and Affiliations

  1. CEMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia

    Diogo A. Gomes

  2. KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering, Thuwal, Saudi Arabia

    Diogo A. Gomes

  3. Electrical and Computer Engineering Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213-3890, USA

    João Saúde

Authors
  1. Diogo A. Gomes
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  2. João Saúde
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Correspondence to Diogo A. Gomes.

Additional information

D. Gomes was partially supported by KAUST baseline and start-up funds and KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering. J. Saúde was partially supported by FCT/Portugal through the CMU-Portugal Program.

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Gomes, D.A., Saúde, J. Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition. Appl Math Optim 83, 51–82 (2021). https://doi.org/10.1007/s00245-018-9510-0

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  • DOI: https://doi.org/10.1007/s00245-018-9510-0

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