A Note on the Power of Truthful Approximation Mechanisms

TL;DR

This paper investigates the limitations of polynomial-time truthful mechanisms compared to non-truthful algorithms, demonstrating scenarios where truthfulness significantly reduces approximation guarantees and highlighting the unbounded cost of ensuring truthfulness.

Contribution

It establishes that in certain settings, truthful mechanisms cannot guarantee bounded approximation ratios, unlike non-truthful algorithms, and introduces a universally truthful mechanism with a ratio of 2.

Findings

Deterministic truthful mechanisms lack bounded approximation guarantees in some settings.

Non-truthful FPTAS exists where truthful mechanisms cannot.

A universally truthful mechanism achieves a 2-approximation in the same setting.

Abstract

We study the power of polynomial-time truthful mechanisms comparing to polynomial time (non-truthful) algorithms. We show that there is a setting in which deterministic polynomial-time truthful mechanisms cannot guarantee a bounded approximation ratio, but a non-truthful FPTAS exists. We also show that in the same setting there is a universally truthful mechanism that provides an approximation ratio of 2. This shows that the cost of truthfulness is unbounded. The proofs are almost standard in the field and follow from known results.