Optimality of linearity with collusion and renegotiation

• We analyze a continuous-time Brownian agency model with constant absolute risk aversion utilities.
• NN-agents determine the mean and variance of the returns.
• Our Brownian agency model features collusion and renegotiation.
• A theoretical justification for linear contracts is provided as in Holmstrom and Milgrom (1987).
• We prove that there exists a linear and stationary optimal compensation scheme.

This study analyzes a continuous-time NN-agent Brownian moral hazard model with constant absolute risk aversion (CARA) utilities, in which agents’ actions jointly determine the mean and variance of the outcome process. In order to give a theoretical justification for the use of linear contracts, as in Holmstrom and Milgrom (1987), we consider a variant of its generalization given by Sung (1995), into which collusion and renegotiation possibilities among agents are incorporated. In this model, we prove that there exists a linear and stationary optimal compensation scheme which is also immune to collusion and renegotiation.