We study the mechanism design for discrete facility location games with different preferences, where the facilities can only be built at a finite set of candidate locations, and a mechanism maps the agent locations to candidate locations for building facilities. We consider both the obnoxious preferences, where the agents want to stay as far away as possible from the facilities, and the dual preferences, where each agent may either like or dislike a facility. When the preferences are obnoxious, for two heterogeneous facilities, we present a group strategy-proof mechanism which has an approximation ratio of 2 for both social utility objective and minimum utility objective. Both objectives are proven to have a lower bound of \(\frac{3}{2}\). For two homogeneous facilities, we prove there is no deterministic strategy-proof mechanism with bounded approximation ratio. When the preferences are dual, we consider the single facility location games under the social utility objective, and propose a group strategy-proof mechanism with approximation ratio of 4.

我们研究了具有不同偏好的离散设施位置游戏的机制设计，其中设施只能在有限的一组候选位置上建造，并且机制将代理位置映射到建造设施的候选位置。我们考虑了令人讨厌的偏好（代理人希望尽可能远离设施）和双重偏好（每个代理人可能喜欢或不喜欢某个设施）。当偏好令人讨厌时，对于两个异构设施，我们提出了一种群体策略证明机制，其社会效用目标和最小效用目标的近似比均为 2。两个目标均被证明具有下限\(\frac{3}{2}\)。对于两个同质设施，我们证明不存在具有有界近似比的确定性策略证明机制。当偏好为双重时，我们考虑社会效用目标下的单设施选址博弈，提出近似比为4的群体策略证明机制。