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On the implementation of the median

Matias Nuñez, Carlos Pimienta and Dimitrios Xefteris

Journal of Mathematical Economics, 2022, vol. 99, issue C

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.

Keywords: Nash implementation; Bayesian implementation; Robust implementation; Median rule; Strategy-proofness; Single-peaked preferences (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:99:y:2022:i:c:s030440682100152x

DOI: 10.1016/j.jmateco.2021.102595

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