Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

A longstanding open problem in algorithmic mechanism design is to design truthful mechanisms that are computationally efficient and (approximately) maximize welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, ACM, New York, 2005, pp. 610–618] who gave an -approximation, where is the number of items. This problem has been studied extensively since, culminating in an -approximation mechanism by Dobzinski [Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, ACM, New York, 2016, pp. 940–948]. We present a computationally-efficient truthful mechanism with an approximation ratio that improves upon the state-of-the-art by an exponential factor. In particular, our mechanism achieves an -approximation in expectation, uses only demand queries, and has universal truthfulness guarantee. This settles an open question of Dobzinski on whether is the best approximation ratio in this setting in the negative.