Too Good to Be True? Retention Rules for Noisy Agents

An agent who privately knows his type seeks to be retained by a principal. Agents signal their type with some ambient noise, but can alter this noise, perhaps at some cost. Our main finding is that in equilibrium, the principal treats extreme signals in either direction with suspicion, and retains the agent if and only if the signal falls in some intermediate bounded set. In short, she follows the maxim: “if it seems too good to be true, it probably is.” We consider extensions and applications, including non-normal signal structures, dynamics with term limits, risky portfolio management, and political risk-taking.