Optimality of linearity with collusion and renegotiation

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This study analyzes a continuous-time N-agent Brownian moral hazard model with constant absolute risk aversion (CARA) utilities, in which agents' actions jointly determine the mean and the 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.