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.