Implementing the Median

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