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On the implementation of the median

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  • Núñez, Matías
  • Pimienta, Carlos
  • Xefteris, Dimitrios

Abstract

In the single-peaked domain, the median rule is strategy-proof but not implementable in (Bayes–)Nash equilibrium by its associated direct mechanism. We define the value-based median mechanism that implements the median rule in (Bayes–)Nash equilibrium in the single-peaked domain under complete and incomplete information. Such a mechanism selects the median of the profile of different values announced by the agents (i.e., ignoring redundant announcements). The value-based median does not depend on agents’ beliefs (in line with robust mechanism design). In the case of incomplete information, it induces truthful revelation of preferences (in line with strategy-proofness) for almost all peaks. We present extensions of our results to generalized median rules and finite policy spaces and their limitations.

Suggested Citation

  • Núñez, Matías & Pimienta, Carlos & Xefteris, Dimitrios, 2022. "On the implementation of the median," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:mateco:v:99:y:2022:i:c:s030440682100152x
    DOI: 10.1016/j.jmateco.2021.102595
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