具有二分偏好的扰民设施选址博弈
The Obnoxious Facility Location Game with Dichotomous Preferences
AI总结：
研究路径上异构扰民设施选址博弈，设计功利主义与平均主义两类防策略机制，给出近似比并证明下界，同时将结果扩展至环和单位正方形。
摘要：
我们考虑一种设施选址博弈，其中 $n$ 个智能体居住在路径上的已知位置，且 $k$ 个异构设施将建在该路径上。每个智能体受到部分设施子集的不利影响，而其他设施对其没有影响。我们设计了两类机制，用于在给定智能体报告偏好的情况下选择设施位置：力求最大化社会福利（即追求效率）的功利主义机制，以及力求最大化最小福利的平均主义机制。对于功利主义目标，我们提出了一种适用于最多三个设施的弱群体防策略的高效机制；给出了强群体防策略机制，在 $k=1$ 和 $k > 1$ 时分别实现了 $5/3$ 和 $2$ 的近似比；并证明了在单一设施情况下，没有强群体防策略机制能实现小于 $5/3$ 的近似比。对于平均主义目标，我们提出了一种适用于任意 $k$ 的防策略平均主义机制，并证明了对于两个设施的情况，没有弱群体防策略机制能实现 $o(\sqrt{n})$ 的近似比。我们将平均主义结果扩展到智能体位于环上的情况，并将第一个平均主义结果扩展到智能体位于单位正方形内的情况。
英文摘要：
We consider a facility location game in which $n$ agents reside at known locations on a path, and $k$ heterogeneous facilities are to be constructed on the path. Each agent is adversely affected by some subset of the facilities, and is unaffected by the others. We design two classes of mechanisms for choosing the facility locations given the reported agent preferences: utilitarian mechanisms that strive to maximize social welfare (i.e., to be efficient), and egalitarian mechanisms that strive to maximize the minimum welfare. For the utilitarian objective, we present a weakly group-strategyproof efficient mechanism for up to three facilities, we give strongly group-strategyproof mechanisms that achieve approximation ratios of $5/3$ and $2$ for $k=1$ and $k > 1$, respectively, and we prove that no strongly group-strategyproof mechanism achieves an approximation ratio less than $5/3$ for the case of a single facility. For the egalitarian objective, we present a strategyproof egalitarian mechanism for arbitrary $k$, and we prove that no weakly group-strategyproof mechanism achieves a $o(\sqrt{n})$ approximation ratio for two facilities. We extend our egalitarian results to the case where the agents are located on a cycle, and we extend our first egalitarian result to the case where the agents are located in the unit square.
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