Implementing the Median

15 Pages Posted: 12 Jul 2018

See all articles by Matias Nuñez

Matias Nuñez

Université Paris Dauphine

Carlos Pimienta

University of New South Wales (UNSW)

Dimitrios Xefteris

University of Cyprus

Date Written: June 24, 2018


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

Suggested Citation

Nuñez, Matias and Pimienta, Carlos and Xefteris, Dimitrios, Implementing the Median (June 24, 2018). UNSW Business School Research Paper No. 2018-11, Available at SSRN: or

Matias Nuñez

Université Paris Dauphine ( email )

Place du Maréchal de Tassigny
Paris, Cedex 16 75775

Carlos Pimienta (Contact Author)

University of New South Wales (UNSW) ( email )

High St
Sydney, NSW 2052

Dimitrios Xefteris

University of Cyprus ( email )

75 Kallipoleos Street
P.O. Box 20537
1678 Nicosia

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