Mechanism design with collusive supervision

We analyze an adverse selection environment with third party supervision. The supervisor is partly informed of the agent's type. The supervisor and the agent collude while interacting with the principal. Contracting with the agent directly and ignoring the presence of the supervisor constitutes the no-supervision benchmark. We show that delegating to the supervisor reduces the principal's payoff compared to the no-supervision benchmark under a standard condition on the distribution of the agent's types. In contrast, if the principal contracts with both the agent and the supervisor, there exists a mechanism that improves the principal's payoff over the no-supervision payoff.