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Prompt mechanism for online auctions with multi-unit demands

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  • Xiangzhong Xiang

    (The University of Hong Kong)

Abstract

We study the following TV ad placement problem: $$m$$ m identical time-slots are on sale within a period of $$m$$ m days and only one time-slot is available each day. Advertisers arrive and depart online to bid for some time-slots to publish their ads. Typically, advertiser $$i$$ i arrives at the $$a_i$$ a i ’th day and wishes that her ad would be published for at most $$s_i$$ s i days before she departs. The goal is to maximize the social welfare which is the sum of values of the published ads. In this paper, we design a competitive online mechanism in which each advertiser is motivated to report her private value truthfully and can learn her payment at the very moment that she wins some time-slots. When all demands $$s_i$$ s i ’s are uniform, we prove that our mechanism achieves a non-trivial competitive ratio of $$5$$ 5 . We also study general cases and derive upper and lower bounds.

Suggested Citation

  • Xiangzhong Xiang, 2015. "Prompt mechanism for online auctions with multi-unit demands," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 335-346, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9754-9
    DOI: 10.1007/s10878-014-9754-9
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    References listed on IDEAS

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    1. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    2. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    3. Tian-Ming Bu & Xiaotie Deng & Qi Qi, 2012. "Multi-bidding strategy in sponsored search auctions," Journal of Combinatorial Optimization, Springer, vol. 23(3), pages 356-372, April.
    4. György Dósa & Leah Epstein, 2010. "Online scheduling with a buffer on related machines," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 161-179, August.
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