IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v11y2020i3p30-d395498.html
   My bibliography  Save this article

Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost

Author

Listed:
  • Zahrate El Oula Frihi

    (Lab. of Probability and Statistics (LaPS), Department of Mathematics, Badji-Mokhtar University, B.P.12, Annaba 23000, Algeria)

  • Julian Barreiro-Gomez

    (Learning & Game Theory Laboratory, Engineering Division, New York University Abu Dhabi, Saadiyat Campus, PO Box 129188, Abu Dhabi 44966, UAE
    Research Center on Stability, Instability and Turbulence, New York University Abu Dhabi, Abu Dhabi 44966, UAE)

  • Salah Eddine Choutri

    (Learning & Game Theory Laboratory, Engineering Division, New York University Abu Dhabi, Saadiyat Campus, PO Box 129188, Abu Dhabi 44966, UAE
    Research Center on Stability, Instability and Turbulence, New York University Abu Dhabi, Abu Dhabi 44966, UAE)

  • Hamidou Tembine

    (Learning & Game Theory Laboratory, Engineering Division, New York University Abu Dhabi, Saadiyat Campus, PO Box 129188, Abu Dhabi 44966, UAE
    Research Center on Stability, Instability and Turbulence, New York University Abu Dhabi, Abu Dhabi 44966, UAE)

Abstract

This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control strategies. We derive the Nash mean-field-type equilibrium and cost in a linear state-and-mean-field feedback form by using a partial integro-differential system. Then, we examine the Stackelberg two-layer problem with multiple leaders and multiple followers. Numerical illustrations show that, in the symmetric case, having only one leader is not necessarily optimal for the total sum cost. Having too many leaders may also be suboptimal for the total sum cost. The methodology is extended to multi-level hierarchical systems. It is shown that the order of the play plays a key role in the total performance of the system. We also identify a specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. In the heterogeneous case, it is shown that the total cost is significantly affected by the design of the hierarchical structure of the problem.

Suggested Citation

  • Zahrate El Oula Frihi & Julian Barreiro-Gomez & Salah Eddine Choutri & Hamidou Tembine, 2020. "Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost," Games, MDPI, vol. 11(3), pages 1-26, August.
    • Handle: RePEc:gam:jgames:v:11:y:2020:i:3:p:30-:d:395498
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/11/3/30/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/11/3/30/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Panayiotis Theodossiou & Christos S. Savva, 2016. "Skewness and the Relation Between Risk and Return," Management Science, INFORMS, vol. 62(6), pages 1598-1609, June.
    2. Jingtao Shi, 2018. "Stochastic Leader-Follower Differential Game with Asymmetric Information," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
    3. 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.
    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. Panayiotis Theodossiou & Polina Ellina & Christos S. Savva, 2022. "Stochastic properties and pricing of bitcoin using a GJR-GARCH model with conditional skewness and kurtosis components," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 695-716, August.
    2. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    3. Karagiorgis, Ariston & Drakos, Konstantinos, 2022. "The Skewness-Kurtosis plane for non-Gaussian systems: The case of hedge fund returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    4. Panayiotis Theodossiou & Dimitris Tsouknidis & Christos Savva, 2020. "Freight rates in downside and upside markets: pricing of own and spillover risks from other shipping segments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1097-1119, June.
    5. Ioannidis, Filippos & Kosmidou, Kyriaki & Savva, Christos & Theodossiou, Panayiotis, 2021. "Electricity pricing using a periodic GARCH model with conditional skewness and kurtosis components," Energy Economics, Elsevier, vol. 95(C).
    6. Zheng, Yueyang & Shi, Jingtao, 2022. "A linear-quadratic partially observed Stackelberg stochastic differential game with application," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    7. Panayiotis Theodossiou, 2015. "Skewed Generalized Error Distribution of Financial Assets and Option Pricing," Multinational Finance Journal, Multinational Finance Journal, vol. 19(4), pages 223-266, December.
    8. Delis, Manthos & Savva, Christos & Theodossiou, Panayiotis, 2020. "A Coronavirus Asset Pricing Model: The Role of Skewness," MPRA Paper 100877, University Library of Munich, Germany.
    9. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Papantonis, Ioannis & Rompolis, Leonidas & Tzavalis, Elias, 2023. "Improving variance forecasts: The role of Realized Variance features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1221-1237.
    11. 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.
    12. Delis, Manthos D. & Savva, Christos S. & Theodossiou, Panayiotis, 2021. "The impact of the coronavirus crisis on the market price of risk," Journal of Financial Stability, Elsevier, vol. 53(C).
    13. Papantonis Ioannis & Tzavalis Elias & Agapitos Orestis & Rompolis Leonidas S., 2023. "Augmenting the Realized-GARCH: the role of signed-jumps, attenuation-biases and long-memory effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(2), pages 171-198, April.
    14. Jun Moon & Wonhee Kim, 2020. "Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models," Mathematics, MDPI, vol. 8(10), pages 1-23, September.
    15. Eero J. Pätäri & Timo H. Leivo & Janne Hulkkonen & J. V. Samuli Honkapuro, 2018. "Enhancement of value investing strategies based on financial statement variables: the German evidence," Review of Quantitative Finance and Accounting, Springer, vol. 51(3), pages 813-845, October.
    16. Juzhi Zhang & Suresh P. Sethi & Tsan‐Ming Choi & T. C. E. Cheng, 2020. "Supply Chains Involving a Mean‐Variance‐Skewness‐Kurtosis Newsvendor: Analysis and Coordination," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1397-1430, June.
    17. Delis, Manthos & Iosifidi, Maria & Tsionas, Mike G, 2017. "Endogenous bank risk and efficiency," European Journal of Operational Research, Elsevier, vol. 260(1), pages 376-387.
    18. Andrew Harvey & Rutger‐Jan Lange, 2018. "Modeling the Interactions between Volatility and Returns using EGARCH‐M," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 909-919, November.
    19. Mazur Błażej & Pipień Mateusz, 2018. "Time-varying asymmetry and tail thickness in long series of daily financial returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-21, December.
    20. Wang, Zijun & Khan, M. Moosa, 2017. "Market states and the risk-return tradeoff," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 314-327.

    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:gam:jgames:v:11:y:2020:i:3:p:30-:d:395498. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.