Heterogeneous Facility Location with Limited Resources

TL;DR

This paper explores designing strategyproof mechanisms for locating a single facility on a line segment with agents having approval preferences, aiming to maximize social welfare under various information settings.

Contribution

It introduces new mechanisms for the heterogeneous facility location problem with limited resources, addressing different information scenarios and providing approximation guarantees.

Findings

Developed deterministic and randomized strategyproof mechanisms.

Achieved near-optimal approximation ratios for social welfare.

Provided tight impossibility bounds for mechanism performance.

Abstract

We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three different settings depending on the level of agent-related information that is public or private. For each setting, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results.