(with Francisco Espinosa), May 2018. Supplementary Appendix
Summary. Agents signal their type in a principal-agent model; the principal seeks to retain good agents. Types are signaled with some ambient noise. Agents can choose to add or remove additional noise at a cost. It is shown that monotone retention strategies, in which the principal keeps the agent if the signal crosses some threshold, are generically never equilibria. The main result identifies an equilibrium with a bounded retention zone, in which the principal is wary of both excessively good and excessively bad signals: she retains the agent if the signal is “moderate” and replaces him otherwise.