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Strategyproof mechanisms for 2-facility location games with minimax envy

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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.

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Acknowledgements

This research was supported partially by the National Natural Science Foundation of China (11971447, 11871442), the Natural Science Foundation of Shandong Province of China (ZR2019MA052) and the Fundamental Research Funds for the Central Universities of China (201964006, 201861001).

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Authors and Affiliations

  1. College of Information Science and Engineering, Ocean University of China, Qingdao, 266100, China

    Xin Chen

  2. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Qizhi Fang, Wenjing Liu, Yuan Ding & Qingqin Nong

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  1. Xin Chen
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  2. Qizhi Fang
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  3. Wenjing Liu
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  4. Yuan Ding
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  5. Qingqin Nong
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Correspondence to Wenjing Liu.

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A preliminary version of this paper appeared in the Proceedings of the 14th International Conference on Algorithmic Aspects in Information and Management (AAIM 2020), Z. Zhang et al. (Eds.), Lecture Notes in Computer Science 12290, Springer, 260–272.

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Chen, X., Fang, Q., Liu, W. et al. Strategyproof mechanisms for 2-facility location games with minimax envy. J Comb Optim 43, 1628–1644 (2022). https://doi.org/10.1007/s10878-021-00711-7

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