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Principal-Agent Problem with Common Agency without Communication

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multiPrincipalRevision.pdf (382.8Kb)
Date
2018
Publishing date
01-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01534611
Dewey
Probabilités et mathématiques appliquées
Sujet
system of HJB equa- tions; BSDEs; Moral hazard models; common agency; system of HJB equations
JEL code
D.D2.D21; D.D8.D82; D.D8.D86; J.J4.J41; C.C7.C73
URI
https://basepub.dauphine.fr/handle/123456789/17975
Collections
  • CEREMADE : Publications
Metadata
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Author
Mastrolia, Thibaut
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Ren, Zhenjie
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
32
Abstract (EN)
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.

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