Everyone is welcome to attend the N&O lecturen of Sahil Singla with the title '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 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((loglog 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 Θ(\sqrt{log m}) is the best approximation ratio in this setting in negative.
This is joint work with Sepehr Assadi and it will appear in FOCS 2019.
