Supervisory Efficiency, Collusion, and Contract Design

We analyze a principal-supervisor-two-agent hierarchy with soft information. The supervisor may be inefficient such that a noisy signal on the agents’ effort levels is observed. On one hand, the agents require risk premiums to work due to the noisy signal. On the other hand, the supervisor and the agents may collude against the principal. We identify a new trade-off between inefficient supervision and supervisor-agent collusion, showing that under certain conditions tolerating collusion to take place helps to “correct” wrong supervisory signals and thus benefits the principal. Furthermore, the characterization of the collusive-supervision contract shows that collusion should be allowed with one agent only.