No truthful mechanism can be better than $n$ approximate for two natural problems

TL;DR

This paper demonstrates that for certain natural network optimization problems, no truthful mechanism can outperform an n-approximation, establishing a fundamental limit in mechanism design for these problems.

Contribution

It introduces the first non-utilitarian problems where the trivial n-approximation via VCG mechanisms is provably optimal.

Findings

No truthful mechanism can achieve better than n-approximation for these problems.

The min-max shortest path and minimum spanning tree problems are used as key examples.

The results set a lower bound on the performance of truthful mechanisms in these settings.

Abstract

This work gives the first natural non-utilitarian problems for which the trivial $n$ approximation via VCG mechanisms is the best possible. That is, no truthful mechanism can be better than $n$ approximate, where $n$ is the number of agents. The problems are the min-max variant of shortest path and (directed) minimum spanning tree mechanism design problems. In these procurement auctions, agents own the edges of a network, and the corresponding edge costs are private. Instead of the total weight of the subnetwork, in the min-max variant we aim to minimize the maximum agent cost.