Mechanism Design for Congested Facility Location

TL;DR

This paper develops strategyproof mechanisms for congested facility location problems involving conflicting agents, achieving optimal or near-optimal social and maximum costs under various misreporting scenarios.

Contribution

It introduces new strategyproof mechanisms tailored for different misreporting types in congested facility location, with proven optimality and approximation bounds.

Findings

Strategyproof mechanisms achieve optimal social cost under location-only misreporting.

Median mechanism attains tight bounds for group membership misreporting.

Novel mechanisms for minimizing maximum cost under various misreporting types.

Abstract

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.