Screening with Endogenous Preferences

A general framework is developed for studying screening in many-agent discrete type environments wherein each agent's preferences depend endogenously on the allocations received by the other agents. Applications include optimal income taxation, performance contracting with across-worker externalities, and insurance with endogenous risks. The solution to the principal's problem is analyzed by decomposing it, a la Rothschild and Scheuer (2013, 2014b), into an inner problem with fixed preferences and an outer problem with varying preferences. The outer problem is typically discontinuous at points where the preferences of two or more types endogenously coincide. As a result, the principal will frequently find it optimal to select allocations which involve two or more types with endogenously coinciding preferences, even though such allocations may appear, ex-ante, to be highly unusual. Assuming that types are strictly ordered by their single-crossing preferences is, therefore, not innocuous in endogenous preference environments