Positive Intra-Group Externalities in Facility Location

We study facility location games with multiple groups in one dimension where an agent's utility is not only decided by the distance from the facility but also by their group members. The positive effect of the interactions within a group is captured by positive intra-group externalities. Our goal is to design a mechanism that is non-manipulable and respects unanimity while (approximately) optimizing an objective function. We consider three types of manipulation, misreporting only the location, misreporting only the group membership, and misreporting both, under two social objectives, the social utility and the minimum utility. For both objectives, we achieve nearly tight bounds by either designing new mechanisms or extending the existing mechanisms in terms of the first two types of manipulation. As to the negative result, we show that strategyproofness and unanimity are incompatible when each agent can misreport both the location and the group membership, which is independent of the objective functions.