Theoretical Economics, Volume 17, Number 3 ( 2022)

Theoretical Economics 17 (2022), 1145–1181

Participation constraints in discontinuous adverse selection models

David Martimort, Lars A. Stole


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 economic environments in contract theory where discontinuities in objectives prevail. Examples of applications include nonlinear pricing of digital goods and nonlinear pricing under competitive threat.

Keywords: Optimal control, non-smooth optimization, convex analysis, type-dependent participation constraints, principal-agent models

JEL classification: D82, D86

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