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Principal-Agent Problem with Common Agency without Communication

Author

Listed:
  • Thibaut Mastrolia

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Zhenjie Ren

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the optimisation problem of the Principals to a system of coupled Hamilton-Jacobi-Bellman (HJB) equations. We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common Agent. In this continuous time model, we extend the result of Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, by showing that these two optimisations coincide only in the first best case. We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the correlation between the projects.

Suggested Citation

  • Thibaut Mastrolia & Zhenjie Ren, 2018. "Principal-Agent Problem with Common Agency without Communication," Working Papers hal-01534611, HAL.
    • Handle: RePEc:hal:wpaper:hal-01534611
    DOI: 10.1137/17M1133609
    Note: View the original document on HAL open archive server: https://hal.science/hal-01534611v2
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    4. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2019. "Optimal make-take fees for market making regulation," Working Papers hal-02379592, HAL.
    5. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    6. Qi Luo & Romesh Saigal, 2020. "Dynamic Multiagent Incentive Contracts: Existence, Uniqueness, and Implementation," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    7. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.

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    More about this item

    Keywords

    system of HJB equations; common agency; Moral hazard models; BSDEs; system of HJB equa- tions;
    All these keywords.

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