Principal-Agent Problem with Common Agency without Communication
Mastrolia, Thibaut; Ren, Zhenjie (2018), Principal-Agent Problem with Common Agency without Communication, SIAM Journal on Financial Mathematics, 9, 2, p. 32. 10.1137/17M1133609
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Financial Mathematics
SIAM - Society for Industrial and Applied Mathematics
MetadataShow full item record
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywordssystem of HJB equa- tions; BSDEs; Moral hazard models; common agency; system of HJB equations
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