Abstract
We study deterministic mechanism design without money for k-facility location games with envy ratio on a real line segment, where a set of strategic agents report their locations and a social planner locates k facilities for minimizing the envy ratio. The objective of envy ratio, which is defined as the maximum over the ratios between any two agents’ utilities, is derived from fair division to measure the fairness with respect to a certain facility location profile.
The problem is studied in two settings. In the homogeneous k-facility location game where k facilities serve the same purpose, we propose a \(\frac{2k}{2k-1}\)-approximate deterministic group strategyproof mechanism which is also the best deterministic strategyproof mechanism. In the heterogeneous k-facility location game where each facility serves a different purpose, when k is even, we devise the optimal and group strategyproof mechanism; when k is odd, we provide a \(\frac{k+1}{k-1}\)-approximate deterministic group strategyproof mechanism.
This research was supported in part 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 (201964006).
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Notes
- 1.
Analogically, in the facility location setting, we can say agent i envies agent j if her cost is greater than j’s, or equivalently her utility is less than j’s. It seems that defining the envy ratio as the maximum over ratios between any two agents’ cost can also represent fairness. We simply follow the way of [6] and give the utility version of the envy ratio. Besides, we conjecture there might not exist any positive results for the cost version of the envy ratio, although without verification.
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Liu, W., Ding, Y., Chen, X., Fang, Q., Nong, Q. (2020). Multiple Facility Location Games with Envy Ratio. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_23
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