Topics in the Design of Political and Economic Mechanisms

Abstract

Finally, the third essay analyzes conditions for the convexifiability of an agent's utility $u(a)$ viewed a function of his type. The study shows that if the set of types A is an m-dimensional rectangle, $m\ge1,$ then u can be assumed convex in a without loss of generality. In particular, in any unidimensional model where A is convex and compact, u is essentially convex. Furthermore, if A is a compact, strictly convex set and its boundary $\partial A$ is a level set of a nonsingular function, the study derives conditions on A and u ensuring that there exists a change of variables H such that $B=H\sp{-1}(A)$ is a convex set and the function $U=u\circ H:B\to\IR$ is strictly convex.