IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i3d10.1007_s10957-025-02664-x.html
   My bibliography  Save this article

Agency Problem and Mean Field System of Agents with Moral Hazard, Synergistic Effects and Accidents

Author

Listed:
  • Thibaut Mastrolia

    (Department of Industrial Engineering and Operations Research)

  • Jiacheng Zhang

    (The Chinese University of Hong Kong Shatin)

Abstract

We investigate the existence of an optimal policy to monitor a mean field system of agents managing a risky project under moral hazard with accidents modeled by Lévy processes magnified by the law of the project. We provide a general method to find both a mean field equilibrium for the agents and the optimal compensation policy under general, sufficient and necessary assumptions on all the parameters. We formalize the problem as a bilevel optimization with the probabilistic version of a mean field games which can be reduced to a controlled McKean-Vlasov SDE with jumps. We apply our results to an optimal energy demand-response problem with a crowd of consumers subjected to power cut/shortage when the variability of the energy consumption is too high under endogenous or exogenous strains. In this example, we get explicit solution to the mean field game and to the McKean-Vlasov equation with jumps.

Suggested Citation

  • Thibaut Mastrolia & Jiacheng Zhang, 2025. "Agency Problem and Mean Field System of Agents with Moral Hazard, Synergistic Effects and Accidents," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-32, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02664-x
    DOI: 10.1007/s10957-025-02664-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02664-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-025-02664-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Working Papers hal-01504473, HAL.
    2. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2021. "Optimal make–take fees for market making regulation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 109-148, January.
    3. Jessica Martin & St'ephane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Papers 2102.00001, arXiv.org.
    4. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    5. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    6. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    7. Yiqing Lin & Zhenjie Ren & Nizar Touzi & Junjian Yang, 2020. "Random horizon principal-agent problems," Papers 2002.10982, arXiv.org, revised Feb 2022.
    8. Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2020. "Mean field games with controlled jump–diffusion dynamics: Existence results and an illiquid interbank market model," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6927-6964.
    9. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    10. Sayan Chatterjee, 1986. "Types of synergy and economic value: The impact of acquisitions on merging and rival firms," Strategic Management Journal, Wiley Blackwell, vol. 7(2), pages 119-139, March.
    11. Steven Campbell & Yichao Chen & Arvind Shrivats & Sebastian Jaimungal, 2021. "Deep Learning for Principal-Agent Mean Field Games," Papers 2110.01127, arXiv.org.
    12. Thibaut Mastrolia, 2017. "Moral hazard in welfare economics: on the advantage of Planner's advices to manage employees' actions," Papers 1706.01254, arXiv.org.
    13. Hartman-Glaser, Barney & Piskorski, Tomasz & Tchistyi, Alexei, 2012. "Optimal securitization with moral hazard," Journal of Financial Economics, Elsevier, vol. 104(1), pages 186-202.
    14. Smith, Richard L & Kim, Joo-Hyun, 1994. "The Combined Effects of Free Cash Flow and Financial Slack on Bidder and Target Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(2), pages 281-310, April.
    15. Sung, Jaeyoung, 1997. "Corporate Insurance and Managerial Incentives," Journal of Economic Theory, Elsevier, vol. 74(2), pages 297-332, June.
    16. Romuald Élie & Emma Hubert & Thibaut Mastrolia & Dylan Possamaï, 2021. "Mean–field moral hazard for optimal energy demand response management," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 399-473, January.
    17. Jessica Martin & Stéphane Villeneuve, 2021. "A Class of Explicit optimal contracts in the face of shutdown," Working Papers hal-03124102, HAL.
    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. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.
    2. Camilo Hernández & Dylan Possamaï, 2024. "Time‐inconsistent contract theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 1022-1085, July.
    3. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    4. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Dec 2024.
    5. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 1-43, June.
    6. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    7. Guillermo Alonso Alvarez & Erhan Bayraktar & Ibrahim Ekren & Liwei Huang, 2024. "Sequential optimal contracting in continuous time," Papers 2411.04262, arXiv.org.
    8. Dena Firoozi & Arvind V Shrivats & Sebastian Jaimungal, 2021. "Principal agent mean field games in REC markets," Papers 2112.11963, arXiv.org, revised Jun 2022.
    9. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    10. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    11. Emma Hubert & Thibaut Mastrolia & Dylan Possamai & Xavier Warin, 2020. "Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic," Papers 2009.00484, arXiv.org, revised Apr 2022.
    12. Jessica Martin & Stéphane Villeneuve, 2023. "Risk-sharing and optimal contracts with large exogenous risks," Post-Print hal-04164688, HAL.
    13. René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
    14. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    15. Rene Carmona, 2020. "Applications of Mean Field Games in Financial Engineering and Economic Theory," Papers 2012.05237, arXiv.org.
    16. Martin Dumav, 2021. "Moral Hazard, Dynamic Incentives, and Ambiguous Perceptions," Papers 2110.15229, arXiv.org.
    17. Thibaut Mastrolia & Zhenjie Ren, 2017. "Principal-Agent Problem with Common Agency without Communication," Papers 1706.02936, arXiv.org, revised Jan 2018.
    18. Thibaut Mastrolia & Tianrui Xu, 2025. "Optimal Rebate Design: Incentives, Competition and Efficiency in Auction Markets," Papers 2501.12591, arXiv.org.
    19. Thibaut Mastrolia & Zhenjie Ren, 2018. "Principal-Agent Problem with Common Agency without Communication," Working Papers hal-01534611, HAL.
    20. Alessandro Chiusolo & Emma Hubert, 2024. "A new approach to principal-agent problems with volatility control," Papers 2407.09471, arXiv.org.

    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:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02664-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.