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A Unifying Framework for Submodular Mean Field Games

Author

Listed:
  • Dianetti, Jodi

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Fischer, Markus

    (Center for Mathematical Economics, Bielefeld University)

  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is allowed. The setting is general enough to encompass qualitatively different problems, such as mean field games for discrete time finite space Markov chains, singularly controlled and reflected diffusions, and mean field games of optimal timing. Our analysis hinges on Tarski's fixed point theorem, along with technical results on lattices of flows of probabiltiy and sub-probability measures.

Suggested Citation

  • Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:661
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    File URL: https://pub.uni-bielefeld.de/download/2960759/2960760
    File Function: First Version, 2022
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    References listed on IDEAS

    as
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    Cited by:

    1. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Papers 2207.00446, arXiv.org, revised Sep 2023.
    2. Robert Denkert & Ulrich Horst, 2023. "Extended mean-field control problems with multi-dimensional singular controls," Papers 2308.04378, arXiv.org.
    3. Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.
    4. Puru Gupta & Saul D. Jacka, 2023. "Portfolio Choice In Dynamic Thin Markets: Merton Meets Cournot," Papers 2309.16047, arXiv.org.

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