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Principal-Agent Problem with Common Agency without Communication

Thibaut Mastrolia and Zhenjie Ren ()
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Thibaut Mastrolia: CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique
Zhenjie Ren: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: system of HJB equa- tions; BSDEs; Moral hazard models; common agency; system of HJB equations (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cta and nep-mic
Date: 2018-01-12
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01534611v2
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