Decentralization of Truthful Revelation and Other Decision Rules

The revelation principle in welfare economics asserts that, in principle, the allocative performance of direct mechanisms (institutions in which an exhaustive report of privately held information is elicited from each agent) is at least as good as that of any other class of institutions. Recently it has been suggested that direct mechanisms may be of practical as well as theoretical importance, although in practice agents would supply only summary information. The distinction between the incentive properties of exhaustive and summary reporting is studied here. The problem of inducing a single person truthfully to report the value of a continuous multidimensional parameter is examined. It is shown that, unless strong restrictions are placed on the person's utility function, the incentive properties of truthful summary reporting about the parameter (e.g., reporting of its first coordinate) are extremely fragile. This assertion of fragility is given a precise statement in terms of topological notions.