Hölder Continuous Implementation

Building upon the classical concept of Holder continuity and the notion of "continuous implementation"introduced in Oury and Tercieux (2009), we define Hölder continuous implementation. We show that, under a richness assumption on the payo proles (associated with outcomes), the following full characterization result holds for finite mechanisms: a social choice function is Hölder continuously implementable if and only if it is fully implementable in rationalizable messages.