A general principal-agent setting with non-differentiable mechanisms: Some examples

A procedure for dealing with monotonicity constraints in optimal control problems is used, within the context of a general model on incentive provision with hidden characteristics, to extend the space of contracts considered in principal-agent theory and thus generalize its results. We conclude that most findings, obtained under assumptions of continuity and piecewise differentiability with respect to the decision variable of the problem, remain valid after replacing such assumptions with two minimal requirements. Examples on monopoly with product quality, countervailing incentives and optimal taxation are also provided to illustrate various sources of non-smoothness in the model, and confirm the adequacy of our methods for deriving the sort of characterization that prevails under the standard conditions of continuity and piecewise differentiability.