Xavier Calsamiglia

A Unique Informationally Efficient and Decentralized Mechanism with Fair Outcomes

It is shown that any informationally decentralized mechanism that realizes fair allocations over the class of classical pure exchange environments has a message space of dimension no smaller than the number of agents times the number of commodities. Since the equal income Walrasian mechanism, in which all agents take prices parametrically and maximize utility subject to the average income constraint, realizes fair outcomes over the class of classical pure exchange environments and has a message space of that dimension, it is informationally efficient. Further, it is shown that it is the unique informationally efficient mechanism realizing fair allocations. Copyright 1993 by The Econometric Society.

On the Size of the Message Space Under Non-Convexities

Abstract In this paper we are concerned with the minimal size of the message space necessary to attain a Pareto efficient allocation through a privacy preserving process in a very simple class of non- convex environments. It is shown that under mild regularity conditions — which do not rule out the use of Peano functions — the message space cannot be σ-compact so that in particular messages cannot be points of a Euclidean space or even the Cartesian product of countably many copies of the closed unit interval.