Abstract:

A number of studies, most notably Cr×mer and McLean (1985, 1988), have shown that in Harsanyi type spaces of a fixed finite size, it is generically possible to design mechanisms that extract all the surplus  from players, and as a consequence, implement any outcome as if the players' private information  were commonly known. In contrast, we show that within the set of common priors on the universal type  space, the subset of priors that permit the extraction of the players' full surplus is shy. Shyness is a  notion of smallness for convex subsets of infinite-dimensional topological vector spaces (in our case,  the set of common priors), which generalizes the usual notion of zero Lebesgue measure in  finite-dimensional spaces.

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