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Journal of Global Optimization

, Volume 70, Issue 4, pp 859–873 | Cite as

Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain

  • Qiaoming Han
  • Donglei Du
  • Dachuan Xu
  • Yicheng Xu
Article

Abstract

The single-dipped domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the dip) in the interval, and the preferences are increasing as one moves away from that dip. Practical domains like this appear in political voting system where each voter has his most-hated candidate and alternative candidates are evaluated by their proximity to this candidate or in obnoxious location problem, where each agent prefers to have the obnoxious location to be distant from his own location, among others. We first characterize deterministic and anonymous strategy-proof and group strategy-proof mechanisms on single-dipped public policy domain, complementing the well-known results on single-peaked policy domain first investigated by Moulin (Pub. Choice 35:437–455, 1980). Then we consider the tradeoff between strategy-proofness and efficiency by applying our characterization. As concrete applications of our results, we extend existing models and results, and resolve several open questions related to the obnoxious facility location game from the algorithmic mechanism design literature.

Keywords

Mechanism design Approximation algorithm Strategy-proof efficiency Pareto-optimal Anonymous 

Notes

Acknowledgements

The first author’s research is supported by the National Natural Science Foundation of China (NSFC grants 11771386 and 11728104) and First Class Discipline A of Zhejiang for Statistics in Zhejiang University of Finance and Economics. The second author’s research is supported by the Natural Science and Engineering Research Council of Canada (NSERC grant 06446) and the National Natural Science Foundation of China (NSFC grant 11728104). The third and fourth authors’ research is supported by the National Natural Science Foundation of China (NSFC grant 11531014). Particularly, we acknowledge the two anonymous referees for their constructive comments to improve the presentation of this paper.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Qiaoming Han
    • 1
  • Donglei Du
    • 2
    • 4
  • Dachuan Xu
    • 3
  • Yicheng Xu
    • 3
  1. 1.School of Data ScienceZhejiang University of Finance and EconomicsHangzhouPeople’s Republic of China
  2. 2.Faculty of Business AdministrationUniversity of New BrunswickFrederictonCanada
  3. 3.Department of Applied MathematicsBeijing University of TechnologyBeijingPeople’s Republic of China
  4. 4.Beijing Institution for Scientific and Engineering ComputingBeijing University of TechnologyBeijingPeople’s Republic of China

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