Group-fair Facility Location Games with Externalities

We study facility location games with externalities where agents are located on a real line and divided into groups. The cost of an agent is affected by the facility location and their group members. The goal is to design mechanisms to locate a facility to approximately optimize group-fair objectives while eliciting the agents' locations truthfully. We consider two types of group interactions: competitive and collaborative, and two group-fair objectives, minimizing the maximum total group cost and minimizing the maximum average group cost. For each scenario, we analyze classic mechanisms, presenting their approximation ratios, and introduce new mechanisms that achieve improved approximation ratios. Additionally, we establish tight lower bounds for each setting, demonstrating that our mechanisms are the best possible. © 2025 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org).