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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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    1. Alvarez E., Luis H.R. & Hening, Alexandru, 2022. "Optimal sustainable harvesting of populations in random environments," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 678-698.
    2. Aïd, René & Basei, Matteo & Ferrari, Giorgio, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Center for Mathematical Economics Working Papers 679, Center for Mathematical Economics, Bielefeld University.
    3. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
    4. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    5. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, December.
    6. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    7. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    8. Andrew Jack & Mihail Zervos, 2006. "A singular control problem with an expected and a pathwise ergodic performance criterion," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-19, June.
    9. Soren Christensen & Berenice Anne Neumann & Tobias Sohr, 2020. "Competition versus Cooperation: A class of solvable mean field impulse control problems," Papers 2010.06452, arXiv.org, revised Apr 2021.
    10. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.
    11. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.
    12. Ren'e Aid & Matteo Basei & Giorgio Ferrari, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Papers 2305.00541, arXiv.org.
    13. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    14. D’Auria, Bernardo & Kella, Offer, 2012. "Markov modulation of a two-sided reflected Brownian motion with application to fluid queues," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1566-1581.
    15. Guanxing Fu & Paul P. Hager & Ulrich Horst, 2023. "Mean-Field Liquidation Games with Market Drop-out," Papers 2303.05783, arXiv.org, revised Sep 2023.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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