Adverse selection without single crossing: Monotone solutions

The single-crossing assumption simplifies the analysis of screening models as local incentive compatibility becomes sufficient for global incentive compatibility. If single crossing is violated, global incentive compatibility constraints have to be taken into account. This paper studies monotone solutions in a screening model that allows a one-time violation of single crossing. The results show that local and non-local incentive constraints distort the solution in opposite directions. Therefore, the optimal decision might involve distortions above as well as below the first-best decision. Furthermore, the well-known “no distortion at the top” property does not necessarily hold. The results show that the decision can even be distorted above first best for all types. Sufficient conditions for existence, (strict) monotonicity and continuity of the solution are presented. A new necessary condition satisfied by such solutions is found. An algorithm based on this condition can calculate continuous and strictly monotone solutions. © 2015 Elsevier Inc. All rights reserved. JEL classification: C61; D82; D86