Implementing the Median

Abstract

In the single-peaked domain, the median rules (Moulin, 1980) are of special interest. They are, essentially, the unique strategy-proof rules as well as the unique Nash implementable ones under complete information. We show that, under mild assumptions on admissible priors, they are also Bayes-Nash implementable by the means of "detail-free'' mechanisms. That is, mechanisms that do not rely on the mechanism designer having detailed information about the priors that the agents hold. Furthermore, detail-free implementation of the median rules does not clash with truthful behavior. The provided mechanism is such that, in every equilibrium, all agents reveal their true peak with probability one.

Keywords: Nash Implementation, Bayesian Implementation, Robust Implementation, Detail-free, Median rule, Strategy-proofness, Single-Peaked Preferences, Condorcet Winner

JEL Classification: C9, D71, D78, H41