Common agency dilemma with information asymmetry in continuous time

In this paper, we consider a problem of contract theory with several Principals hiring a common Agent in the continuous time setting. We more particularly show that optimal contracts satisfy some equilibrium conditions and we reduced the problem of the Principals to a system of fully coupled HJB equations. We illustrate our study in a linear-quadratic model by considering two interacting Principals proposing to hire a common Agent with appetence parameters. We also give conditions ensuring that the optimal effort of the Agent in a non-cooperative Principals model coincides with the optimal effort of the Agent in the aggregate model.

Joint work with Zhenjie Ren.