Truthful Two-Facility Location with Candidate Locations

TL;DR

This paper investigates a strategyproof mechanism design for a two-facility location problem on a line, aiming to optimize social objectives while ensuring agents report their private positions truthfully.

Contribution

It introduces bounds on the approximation ratios of deterministic strategyproof mechanisms for placing two facilities with known candidate locations, considering agents' preferences.

Findings

Established bounds on social cost approximation ratios.

Analyzed mechanisms for different preference classes.

Provided insights into truthful facility placement strategies.

Abstract

We study a truthful two-facility location problem in which a set of agents have private positions on the line of real numbers and known approval preferences over two different facilities. Given the locations of the two facilities, the cost of an agent is the total distance from the facilities she approves. The goal is to decide where to place the facilities from a given finite set of candidate locations so as to (a) approximately optimize desired social objectives, and (b) incentivize the agents to truthfully report their private positions. We focus on the class of deterministic strategyproof mechanisms and show bounds on their approximation ratio in terms of the social cost (i.e., the total cost of the agents) and the max cost for several classes of instances depending on the preferences of the agents over the facilities.