DP15251 Participation Constraints in Discontinuous Adverse Selection Models

Author(s): David Martimort, Lars Stole
Publication Date: September 2020
Keyword(s): convex analysis, non-smooth optimization, Optimal Control, Principal-Agent Models, type-dependent participation constraints
JEL(s): D82
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=15251

We present a set of necessary and sufficient conditions for a class of optimal control problems with pure state constraints for which the objective function is linear in the state variable but the objective function is only required to be upper semi-continuous in the control variable. We apply those conditions to a number of economic environments in contract theory where discontinuities in objectives prevail. Examples of applications include nonlinear pricing of digital goods, nonlinear pricing under competitive threat, and common agency models of regulation.