On the informational size of message spaces

In a recent paper, Mount and Reiter established that, in a certain sense, the competitive mechanism is an "informationally most efficient" procedure for allocating resources. This result, of course, depends upon the way in which we characterize the notion of informational efficiency. Several alternative characterizations, and the relationships among them, are given here, and it is shown under which characterizations the above result is true, and under which it is false. It is shown that there is an intuitively appealing "best" characterization for which it is true.