Agent-Constrained Truthful Facility Location Games

TL;DR

This paper studies strategyproof mechanisms for facility location problems with agents reporting private locations, providing tight bounds on approximation ratios for social cost in both sum and max variants.

Contribution

It introduces tight bounds on the approximation ratios of strategyproof mechanisms for truthful facility location on a line, considering both sum and max cost variants.

Findings

Established tight bounds on approximation ratios for sum-variant.

Established tight bounds on approximation ratios for max-variant.

Mechanisms are proven strategyproof with optimal approximation bounds.

Abstract

We consider a truthful facility location problem in which there is a set of agents with private locations on the line of real numbers, and the goal is to place a number of facilities at different locations chosen from the set of those reported by the agents. Given a feasible solution, each agent suffers an individual cost that is either its total distance to all facilities (sum-variant) or its distance to the farthest facility (max-variant). For both variants, we show tight bounds on the approximation ratio of strategyproof mechanisms in terms of the social cost, the total individual cost of the agents.