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Approximation strategy-proof mechanisms for obnoxious facility location on a line

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Listed:
  • Lili Mei

    (Zhejiang University)

  • Deshi Ye

    (Zhejiang University)

  • Yong Zhang

    (Chinese Academy of Sciences
    The University of Hong Kong)

Abstract

In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible.

Suggested Citation

  • Lili Mei & Deshi Ye & Yong Zhang, 2018. "Approximation strategy-proof mechanisms for obnoxious facility location on a line," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 549-571, August.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-016-0105-x
    DOI: 10.1007/s10878-016-0105-x
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    References listed on IDEAS

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    1. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    2. Noga Alon & Michal Feldman & Ariel D. Procaccia & Moshe Tennenholtz, 2010. "Strategyproof Approximation of the Minimax on Networks," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 513-526, August.
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    4. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    5. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    6. Berman, Oded & Drezner, Zvi, 2000. "A note on the location of an obnoxious facility on a network," European Journal of Operational Research, Elsevier, vol. 120(1), pages 215-217, January.
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    Cited by:

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    2. Deligkas, Argyrios & Filos-Ratsikas, Aris & Voudouris, Alexandros A., 2023. "Heterogeneous facility location with limited resources," Games and Economic Behavior, Elsevier, vol. 139(C), pages 200-215.

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