Sweet Lemons: On Collusion in Hierarchical Agency

We study a principal-supervisor-agent relationship in which the agent and the supervisor may collude. The supervisor observes an informative signal about the agent's privately known production costs. We show that despite collusion the principal (virtually) achieves the profit she would obtain if the supervisor's information was directly available to her. Our mechanism consists of two stages: first payments are randomly determined and only the supervisor is informed about the realization. Then agent and supervisor are asked to report their respective private information. Informing the supervisor about the realized payment schedule endogenously creates asymmetric information between supervisor and agent, preventing the parties from reaching a profitable collusive side-agreement. Contrary to other findings in the literature, a better informed supervisor always makes the principal strictly better off. Our results challenge commonly applied restrictions in mechanism design with collusion: simple extrapolations of `direct' mechanisms where at a single stage all informed agents simultaneously send reports can be strictly sub-optimal.