Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types

Abstract

We extend the conditions for incentive compatibility in mechanism design problems to a more general structure of preferences than that found in the literature, for the case where type is one-dimensional but the outcome function becomes multidimensional. This is so, at least, as long as preferences can be represented by means of sub-utility functions, it is adopted a weak single-crossing property and direct mechanisms turn out to be differentiable. When direct mechanisms are not differentiable, local incentive conditions still remain fully incentive compatible, provided utility is weakly separable in the outcome function, or else, it exhibits linearity in the type.