An Impossibility Result for Truthful Combinatorial Auctions with Submodular Valuations

TL;DR

This paper proves that any universally truthful randomized mechanism approximating social welfare in combinatorial auctions with submodular valuations within a certain factor must use exponentially many value queries, highlighting fundamental limitations.

Contribution

The paper introduces a novel direct hardness approach to establish impossibility results in truthful mechanism design, bypassing complex characterization steps.

Findings

Any mechanism with the specified approximation ratio requires exponential queries.

Impossibility results for polynomial-time truthful mechanisms in combinatorial public projects.

First bounds on the power of truthful-in-expectation mechanisms in this setting.

Abstract

We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides $m^{\frac 1 2 -\epsilon}$ approximation to the social welfare and uses value queries only must use exponentially many value queries, where $m$ is the number of items. In contrast, ignoring incentives there exist constant ratio approximation algorithms for this problem. Our approach is based on a novel \emph{direct hardness} approach and completely skips the notoriously hard characterization step. The characterization step was the main obstacle for proving impossibility results in algorithmic mechanism design so far. We demonstrate two additional applications of our new technique: (1) an impossibility result for universally-truthful polynomial time flexible combinatorial public projects and (2) an impossibility result for truthful-in-expectation mechanisms for exact combinatorial public projects. The latter is the first result that bounds the power of polynomial-time truthful in expectation mechanisms in any setting.