Strategy-Proof Allocation Mechanisms at Differentiable Points

TLDR: In this article, the authors characterize for the restricted domains associated with economic environments strategy-proof allocation mechanisms at points at which they are differentiable with respect to agents' preferences, where the set of attainable alternatives is a subset of a i-dimensional Euclidean space, and the domain of admissible preference n -tuples is restricted.

Abstract: Consider allocation mechanisms that are single valued and where each agent's strategy space is a set of a priori admissible utility functions Such an allocation mechanism is strategy-proof if, for each agent, faithfully reporting his true utility function is a dominant strategy The purpose of this paper is to characterize for the restricted domains associated with economic environments strategy-proof allocation mechanisms at points at which they are differentiable with respect to agents' preferences Our concern with classical economic environments dictates a framework in which (a) the set of attainable alternatives is a subset of a i-dimensional Euclidean space, (b) the domain of admissible preference n -tuples is restricted (utility functions may be required to satisfy such properties as continuity, monotonicity, and quasiconcavity), and (c) the standard representations of economies are admissible; in particular, the analysis applies to economies with and without production, with and without public goods, and with and without externalities Indeed, our goal has been to provide a result on strategy-proofness that is as basic for allocation mechanisms within economic environments as the Gibbard-Satterthwaite Theorem (Gibbard 1973 and Satterthwaite 1975) is for voting procedures with unrestric