Building upon the classical concept of H older continuity and the notion
of \continuous implementation"introduced in Oury and Tercieux (2009), we
de ne H older continuous implementation. We show that, under a richness
assumption on the payo pro les (associated with outcomes), the following
full characterization result holds for nite mechanisms: a social choice function
is H older continuously implementable if and only if it is fully implementable
in rationalizable messages.no
