Working Paper: CEPR ID: DP15251
Authors: David Martimort; Lars Stole
Abstract: 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.
Keywords: Optimal Control; Nonsmooth Optimization; Convex Analysis; Type-Dependent Participation Constraints; Principal-Agent Models
JEL Codes: D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Participation constraints (D10) | Optimal contract design (D86) |
| Discontinuities in objective function (D59) | Non-standard equilibria in contract theory (D86) |
| Typed-dependent participation constraints (Y80) | Optimal control solutions (C61) |
| Participation constraints (D10) | Incentives of agents (L85) |
| Optimal contracts (D86) | Economic behaviors (E70) |
| Discontinuities (D52) | Reevaluation of existing theories in contract design (D86) |