Optimal contracts under competition when uncertainty from adverse selection and moral hazard are present

In a continuous-time setting where a risk-averse agent controls the drift of an output process driven by a Brownian motion, optimal contracts are linear in the terminal output; this result is well-known in a setting with moral hazard and - under stronger assumptions - adverse selection. We show that this result continues to hold when in addition reservation utilities are type-dependent. This type of problem occurs in the study of optimal compensation problems involving competing principals.