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Strategyproof mechanisms for 2-facility location games with minimax envy

Author

Listed:
  • Xin Chen

    (Ocean University of China)

  • Qizhi Fang

    (Ocean University of China)

  • Wenjing Liu

    (Ocean University of China)

  • Yuan Ding

    (Ocean University of China)

  • Qingqin Nong

    (Ocean University of China)

Abstract

We study a fairness-based model for 2-facility location games on the real line where the social objective is to minimize the maximum envy over all agents. All the agents seek to minimize their personal costs, and the envy between any two of them is the difference in their personal costs. We consider two cases of personal costs, called min-dist cost and sum-dist cost. We are interested in pursuing strategyproof mechanisms for 2-facility location games in both cases. For the min-dist personal cost, we first show that a lower bound of the additive approximation for any deterministic strategyproof mechanism is 1/4, then devise a deterministic group strategyproof mechanism with additive approximation of 1/2 and two randomized strategyproof mechanisms with additive approximation of 1/4. For the sum-dist personal cost, we devise a group strategyproof deterministic mechanism which is also optimal.

Suggested Citation

  • Xin Chen & Qizhi Fang & Wenjing Liu & Yuan Ding & Qingqin Nong, 2022. "Strategyproof mechanisms for 2-facility location games with minimax envy," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1628-1644, July.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:5:d:10.1007_s10878-021-00711-7
    DOI: 10.1007/s10878-021-00711-7
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    References listed on IDEAS

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    1. Qiang Zhang & Minming Li, 2014. "Strategyproof mechanism design for facility location games with weighted agents on a line," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 756-773, November.
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    5. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    6. 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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    Cited by:

    1. Qi Zhao & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2023. "Constrained heterogeneous facility location games with max-variant cost," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-20, April.

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