A Note on the Power of Truthful Approximation Mechanisms

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.