We study the two-opposite-facility location game on a line segment, where a mechanism determines the locations of a popular facility and an obnoxious facility for finitely many agents. The agents report their private locations, and try to maximize their own utilities depending on their distances to the facilities. We prove tight bounds on the inapproximability of both randomized and deterministic strategy-proof mechanisms for maximizing the total agent utility minus a penalty determined by the distance between the two facilities.

中文翻译：

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两对立设施位置博弈中策略证明机制的严格效率下界

我们研究线段上的两个相对设施的位置博弈，其中一种机制确定了一个流行设施的位置和一个有限的代理商的讨厌设施的位置。代理商报告自己的私人位置，并根据与设施之间的距离尝试最大化其自身的效用。我们证明了最大化总代理效用的随机和确定性策略证明机制的不可逼近性有一个严格的界限，这要减去两个设施之间的距离所决定的惩罚。