Improved truthful mechanisms for combinatorial auctions with submodular bidders

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 ([EQUATION])-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 almost 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.