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Stationary Discounted and Ergodic Mean Field Games of Singular Control

Author

Listed:
  • Cao, Haoyang

    (Center for Mathematical Economics, Bielefeld University)

  • Dianetti, Jodi

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an erodic performance criterion. This class of games finds natural applications in the context of optimal productivity expansion in dynamic oligopolies. We prove existence and uniqueness of the mean field equilibria for the discounted and the ergodic games by showing the validity of an Abelian limit. The latter allows also to approximate Nash equilibria of - so far unexplored - symmetric N-player ergodic singular control games through the mean field equilibrium of the discounted game. Numerical examples finally illustrate in a case study the dependency of the mean field equilibria with respect to the parameters of the games.

Suggested Citation

  • Cao, Haoyang & Dianetti, Jodi & Ferrari, Giorgio, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Center for Mathematical Economics Working Papers 650, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:650
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    File URL: https://pub.uni-bielefeld.de/download/2955165/2955166
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    References listed on IDEAS

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    2. 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.

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