Improved Truthful Mechanisms for Subadditive Combinatorial Auctions: Breaking the Logarithmic Barrier

TL;DR

This paper introduces a new truthful mechanism for combinatorial auctions with subadditive bidders that significantly improves the approximation ratio to welfare maximization, breaking a long-standing logarithmic barrier and simplifying existing mechanisms.

Contribution

It presents a computationally-efficient truthful mechanism achieving an $O((\log\log m)^3)$-approximation, surpassing the previous $O(\log mig floor$ barrier, and simplifies mechanisms for submodular bidders.

Findings

Achieves $O((\log\log m)^3)$-approximation to welfare in expectation.

Uses only $O(n)$ demand queries, making it computationally efficient.

Simplifies existing mechanisms for submodular bidders.

Abstract

We present a computationally-efficient truthful mechanism for combinatorial auctions with subadditive bidders that achieves an $O((\log\!\log{m})^3)$-approximation to the maximum welfare in expectation using $O(n)$ demand queries; here $m$ and $n$ are the number of items and bidders, respectively. This breaks the longstanding logarithmic barrier for the problem dating back to the $O(\log{m}\cdot\log\!\log{m})$-approximation mechanism of Dobzinski from 2007. Along the way, we also improve and considerably simplify the state-of-the-art mechanisms for submodular bidders.