Strategyproof Facility Location for Five Agents on a Circle using PCD

TL;DR

This paper analyzes a strategyproof facility location mechanism for five agents on a circle, establishing a tight bound for its performance and hypothesizing its approximation ratio for larger odd numbers.

Contribution

It provides a precise bound for the PCD strategyproof mechanism with five agents on a circle and explores its potential for larger odd agent counts.

Findings

Established a tight bound for the PCD mechanism with five agents.

Used optimization techniques to analyze the mechanism's performance.

Hypothesized the approximation ratio for general odd n.

Abstract

We consider the strategyproof facility location problem on a circle. We focus on the case of 5 agents, and find a tight bound for the PCD strategyproof mechanism, which selects the reported location of an agent in proportion to the length of the arc in front of it. We methodically "reduce" the size of the instance space and then use standard optimization techniques to find and prove the bound is tight. Moreover we hypothesize the approximation ratio of PCD for general odd $n$.