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Frontiers of Computer Science

, Volume 13, Issue 2, pp 333–342 | Cite as

Optimal bundles for sponsored search auctions via bracketing scheme

  • Zheng-Dong Xia
  • Tian-Ming BuEmail author
  • Wen-Hui Gong
Research Article
  • 7 Downloads

Abstract

Sponsored search auction has been recently studied and auctioneer’s revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method.We prove that finding a bracketing scheme that maximizes the auctioneer’s revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with K-anonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.

Keywords

sponsored search auction revenue maximization bracketing scheme NP-hardness 

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Notes

Acknowledgements

We would like to thank the anonymous reviewers for their many insightful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 61672012).

Supplementary material

11704_2017_6102_MOESM1_ESM.ppt (112 kb)
Supplementary material, approximately 112 KB.

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghaiChina

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