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Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)

Author

Listed:
  • Dianetti, Jodi

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Tzouanas, Ioannis

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion. The mean-field interaction is of scalar type and it is given through the stationary distribution of the population. Via a constructive approach, we prove the existence and uniqueness of the stationary mean-field equilibrium. Furthermore, we show that this realizes a symmetric $\varepsilon_N$-Nash equilibrium for a suitable ergodic $N$-player game with singular controls. The proof hinges on the characterization of the optimal solution to the representative player's ergodic singular stochastic control problem with regime switching, which is of independent interest and appears here for the first time.

Suggested Citation

  • Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:681
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    File URL: https://pub.uni-bielefeld.de/download/2981284/2981285
    File Function: First Version, 2023
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    References listed on IDEAS

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    Cited by:

    1. Federico Cannerozzi & Giorgio Ferrari, 2024. "Cooperation, Correlation and Competition in Ergodic N-player Games and Mean-field Games of Singular Controls: A Case Study," Papers 2404.15079, arXiv.org, revised Apr 2025.
    2. Cannerozzi, Federico & Ferrari, Giorgio, 2024. "Cooperation, Correlation and Competition in Ergodic $N$-Player Games and Mean-Field Games of Singular Controls: A Case Study," Center for Mathematical Economics Working Papers 691, Center for Mathematical Economics, Bielefeld University.
    3. Sören Christensen & Ernesto Mordecki & Facundo Oliú, 2025. "Two sided ergodic singular control and mean-field game for diffusions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(1), pages 241-267, June.
    4. Robert Denkert & Ulrich Horst, 2024. "Extended mean-field games with multi-dimensional singular controls and non-linear jump impact," Papers 2402.09317, arXiv.org, revised Nov 2024.

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