Efficient allocation of heterogenous commodities with balanced transfers

In this article, we characterize heterogenous commodities allocation problems where an efficient rule can be implemented in dominant strategies with balanced transfers. We show that the class of such problems is non-trivial and that the associated difference domain is one-dimensional. If the domain satisfies convexity, there exists a permutation of the objects for which the associated difference domain is a straight line passing through the origin with positive slope. An interesting feature of the domains is that at most two orderings of the commodities are permissible and, in particular, one ordering must be the reverse of the other.