# Agent-constrained truthful facility location games

## TL;DR

This paper studies how to place facilities truthfully on a number line while minimizing the total cost for agents based on their distances to the facilities.

## Contribution

The paper provides tight bounds on the approximation ratio of strategyproof mechanisms for two cost variants in facility location games.

## Key findings

- Tight bounds for the sum-variant of individual costs are established.
- Tight bounds for the max-variant of individual costs are also derived.

## Abstract

We consider a truthful facility location game 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.