Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders
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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^2m)-approximation where m is the number of items. This problem has been studied extensively since, culminating in an O(√(logm))-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((loglogm)^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(√(logm)) is the best approximation ratio in this setting in negative.
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