Decentralized resource allocation and increasing returns

We study the possibility of designing a decentralized resource allocation mechanism that yields optimal solutions in economies with increasing returns. After a brief review of the mechanisms already designed to cope with nonconvexities, we find out that either they fail to provide efficient solutions in Koopmans' sense, or else they use extremely complex messages. The question arises whether it is possible to define a nonwasteful and privacy-preserving mechanism over a class of environments with increasing returns using finite-dimensional vectors as messages. We show that the answer is no.