Before revision:  Further, in a more specific linear-quadratic model where two interacting Principals hire one common Agent , we are able to calculate the optimal effort by the Agent for both Principals .
After revision:  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 , we are able to calculate the optimal effort by the Agent for both Principals .