Mechanism Design for Congested Facility Location

This paper investigates mechanism design for congested facility location problems, where agents are partitioned into groups with conflicting interests (e.g., competition for booking a basketball court in a gymnasium), and each agent's cost increases when the facility is located closer to their competitors. We analyze three types of misreporting: location-only, group-membership-only, and combined misreporting. To minimize social cost, we propose a strategyproof mechanism that achieves optimality under location-only misreporting. For group membership and combined misreporting, we show that the median mechanism attains tight approximation bounds. For the objective of minimizing maximum cost, we introduce novel strategyproof mechanisms for location-only and group-membership-only misreporting, while employing the leftmost mechanism under combined misreporting. We prove that all proposed mechanisms achieve nearly tight performance guarantees.