Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

TL;DR

This paper introduces a new truthful mechanism for combinatorial auctions with submodular bidders, achieving a significantly better approximation ratio than previous methods, and resolving an open question in the field.

Contribution

It presents a computationally-efficient, universally truthful mechanism with an $O((\log\log{m})^3)$-approximation, improving the best known ratio exponentially and answering an open problem.

Findings

Achieves $O((\log\log{m})^3)$-approximation in expectation

Uses only $O(n)$ demand queries

Provides universal truthfulness guarantee

Abstract

A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an $O(\log^2{m})$-approximation where $m$ is the number of items. This problem has been studied extensively since, culminating in an $O(\sqrt{\log{m}})$-approximation mechanism by Dobzinski [STOC'16]. We present a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor. In particular, our mechanism achieves an $O((\log\log{m})^3)$-approximation in expectation, uses only $O(n)$ demand queries, and has universal truthfulness guarantee. This settles an open question of Dobzinski on whether $\Theta(\sqrt{\log{m}})$ is the best approximation ratio in this setting in negative.