Ironing Without Control

Abstract

I extend Myerson's (1981) ironing technique to more general objective functions. The approach can be used to solve quasilinear principal-agent models with a one-dimensional type in the general case where the monotonicity constraint implied by incentive compatibility may be binding at the optimum. It is based on calculating for each type of the agent a score that takes into account virtual surplus (i.e., aggregate surplus and the agent's information rent) and any distortions that the allocation of the current type causes for the other types through the monotonicity constraint. Optimal allocation rules can be found by maximizing the score of each type independently of other types. With continuous types, the approach is applicable if the virtual surplus (1) satisfies a separability condition, or (2) has nonincreasing marginal returns in the allocation. Under (1) the set of feasible allocations can be an arbitrary fully ordered set, whereas under (2) it can be either an interval or discrete. Unlike in optimal control theory, no assumptions about allocation rules are needed beyond monotonicity. There are analogous results for problems with discrete types.