IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/706.html
   My bibliography  Save this paper

Stationary Mean-Field Games of Singular Control under Knightian Uncertainty

Author

Listed:
  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

  • Tzouanas, Ioannis

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô-diffusion via onesided singular stochastic control, aiming to maximize a long-term average expected profit criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic (zero-sum) game, where the decision maker chooses the ‘best’ singular control policy, while the adversarial player selects the ‘worst’ probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we present an example of mean-field optimal extraction of natural resources under uncertainty and we analyze the impact of uncertainty on the mean-field equilibrium.

Suggested Citation

  • Ferrari, Giorgio & Tzouanas, Ioannis, 2025. "Stationary Mean-Field Games of Singular Control under Knightian Uncertainty," Center for Mathematical Economics Working Papers 706, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:706
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/3003604/3003605
    File Function: First Version, 2025
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    2. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    3. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    4. Asaf Cohen, 2019. "Brownian Control Problems for a Multiclass M/M/1 Queueing Problem with Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 739-766, May.
    5. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    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. 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.
    8. Jodi Dianetti & Giorgio Ferrari & Renyuan Xu, 2024. "Exploratory Optimal Stopping: A Singular Control Formulation," Papers 2408.09335, arXiv.org, revised Oct 2024.
    9. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    10. Alessandro Calvia & Salvatore Federico & Giorgio Ferrari & Fausto Gozzi, 2024. "Existence and uniqueness results for a mean-field game of optimal investment," Papers 2404.02871, arXiv.org, revised Nov 2024.
    11. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    12. 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.
    13. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2023. "Stationary Discounted and Ergodic Mean Field Games with Singular Controls," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 1871-1898, November.
    14. 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.
    15. Jodi Dianetti & Giorgio Ferrari & Markus Fischer & Max Nendel, 2023. "A Unifying Framework for Submodular Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1679-1710, August.
    16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    17. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    18. Clark, Colin W & Clarke, Frank H & Munro, Gordon R, 1979. "The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment," Econometrica, Econometric Society, vol. 47(1), pages 25-47, January.
    19. 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.
    20. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.
    21. 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.
    22. 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.
    23. P. Cardaliaguet, 2013. "Long Time Average of First Order Mean Field Games and Weak KAM Theory," Dynamic Games and Applications, Springer, vol. 3(4), pages 473-488, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    3. 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.
    4. 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.
    5. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    6. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    7. Gualdi, Stanislao & Mandel, Antoine, 2016. "On the emergence of scale-free production networks," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 61-77.
    8. 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.
    9. Yoshifumi Konishi & Nori Tarui, 2015. "Emissions Trading, Firm Heterogeneity, and Intra-industry Reallocations in the Long Run," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(1), pages 1-42.
    10. Erzo G.J. Luttmer, 2010. "Models of Growth and Firm Heterogeneity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 547-576, September.
    11. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    12. Farzad Pourbabaee, 2022. "Robust experimentation in the continuous time bandit problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 151-181, February.
    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. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    15. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
    16. Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    17. Romain Blanchard & Laurence Carassus, 2017. "Convergence of utility indifference prices to the superreplication price in a multiple-priors framework," Papers 1709.09465, arXiv.org, revised Oct 2020.
    18. Driouchi, Tarik & Trigeorgis, Lenos & So, Raymond H.Y., 2020. "Individual antecedents of real options appraisal: The role of national culture and ambiguity," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1018-1032.
    19. Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus Schweizer & Mitja Stadje, 2025. "Robust Multiple Stopping—A Duality Approach," Mathematics of Operations Research, INFORMS, vol. 50(2), pages 1250-1276, May.
    20. Laeven, R.J.A. & Schoenmakers, John G.M. & Schweizer, Nikolaus & Stadje, M.A., 2024. "Robust multiple stopping — A duality approach," Other publications TiSEM 132c6688-3f07-47d8-a4dc-b, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    stationary mean-field games; singular control; model uncertainty; ergodic criterion; freeboundary problem; shooting method;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:706. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.