TY - GEN
T1 - Breaking the logarithmic barrier for truthful combinatorial auctions with submodular bidders
AU - Dobzinski, Shahar
N1 - Publisher Copyright: © 2016 ACM. 978-1-4503-4132-5/16/06...$15.00.
PY - 2016/6/19
Y1 - 2016/6/19
N2 - We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of O(log2 m) [STOC'06], where m is the number of items. This was subsequently improved to an approximation factor of O(log mlog log m) [Dobzinski, APPROX'07] and then to O(log m) [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of O(√log m). Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a.fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.
AB - We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of O(log2 m) [STOC'06], where m is the number of items. This was subsequently improved to an approximation factor of O(log mlog log m) [Dobzinski, APPROX'07] and then to O(log m) [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of O(√log m). Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a.fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.
UR - http://www.scopus.com/inward/record.url?scp=84979201732&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/2897518.2897569
DO - https://doi.org/10.1145/2897518.2897569
M3 - منشور من مؤتمر
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 940
EP - 948
BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
A2 - Mansour, Yishay
A2 - Wichs, Daniel
T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
Y2 - 19 June 2016 through 21 June 2016
ER -