A UNIQUE INFORMATIONALLY EFFICIENT AND DECENTRALIZED MECHANISM WITH FAIR OUTCOMES

It is shown that any informationally decentralized mechanism that real izes fair allocations over the class of classical pure exchange enviro nments has a message space of dimension no smaller than the number of agents times the number of commodities. Since the equal income Walrasi an mechanism, in which all agents take prices parametrically and maxim ize utility subject to the average income constraint, realizes fair ou tcomes over the class of classical pure exchange environments and has a message space of that dimension it is informationally efficient. Fur ther, it is shown that it is the unique informationally efficient mech anism realizing fair allocations.