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Principal-Agent Problem with Common Agency without Communication

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  • Thibaut Mastrolia

    (CMAP)

  • Zhenjie Ren

    (CEREMADE)

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, 2017. "Principal-Agent Problem with Common Agency without Communication," Papers 1706.02936, arXiv.org, revised Jan 2018.
    • Handle: RePEc:arx:papers:1706.02936
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    References listed on IDEAS

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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. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    3. Omar El Euch & Thibaut Mastrolia & Mathieu Rosenbaum & Nizar Touzi, 2019. "Optimal make-take fees for market making regulation," Working Papers hal-02379592, HAL.
    4. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    5. Qi Luo & Romesh Saigal, 2020. "Dynamic Multiagent Incentive Contracts: Existence, Uniqueness, and Implementation," Mathematics, MDPI, vol. 9(1), pages 1-17, December.
    6. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    7. 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.
    8. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.

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