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Prompt mechanism for online auctions with multi-unit demands

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Abstract

We study the following TV ad placement problem: \(m\) identical time-slots are on sale within a period of \(m\) 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 \(i\) arrives at the \(a_i\)’th day and wishes that her ad would be published for at most \(s_i\) 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 are uniform, we prove that our mechanism achieves a non-trivial competitive ratio of \(5\). We also study general cases and derive upper and lower bounds.

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Notes

  1. In the whole paper, we consider the scenario that each advertiser is only interested in publishing her ad on some consecutive days. Note that even if advertisers can publish ads on days which are not consecutive, our prompt mechanism still works and has the same competitive ratio; but our lower bound on the competitive ratio does not hold in such model.

  2. To utilize time-slots efficiently, any rational publisher will not allocate advertiser \(i\) more than \(s_i\) time-slots.

  3. When \(m\) is not a multiple of \(s\), introduce some dummy slots which will not be used by any advertiser.

  4. Group \(G_j\) is totally included in time window \(W_i=[a_i,d_i]\) if and only if \(a_i \le (j-1)\cdot s+1\) and \(d_i \ge j\cdot s\).

  5. This is because \(i\) can win one group when bidding \(v_i\) and \(p\) is the least value \(i\) can bid to win one group.

References

  • Aggarwal G, Goel G, Karande C, Mehta A (2011) Online vertex-weighted bipartite matching and single-bid budgeted allocations. In Proceedings of the twenty-second annual ACM-SIAM symposium on discrete algorithms, SIAM 1253–1264

  • Aggarwal G, Hartline J (2006) Knapsack auctions. In: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, ACM, 1083–1092

  • Archer A, Tardos É (2001) Truthful mechanisms for one-parameter agents. In Foundations of Computer Science, Proceedings. 42nd IEEE Symposium on, IEEE, 482–491

  • Azar Y, Khaitsin E (2011) Prompt mechanism for ad placement over time. Algorithmic Game Theory 6982:19–30

    Article  MathSciNet  Google Scholar 

  • Bartal Y, Chin F, Chrobak M, Fung S, Jawor W, Lavi R, Sgall J, Tichỳ T (2004) Online competitive algorithms for maximizing weighted throughput of unit jobs. STACS 2996:187–198

    Google Scholar 

  • Borgs C, Chayes J, Etesami O, Immorlica N, Jain K, Mahdian M (2007) Dynamics of bid optimization in online advertisement auctions. In Proceedings of the 16th international conference on World Wide Web, ACM, 531–540

  • Bu T-M, Deng X, Qi Q (2012) Multi-bidding strategy in sponsored search auctions. J Comb Optim 23(3):356–372

    Article  MATH  MathSciNet  Google Scholar 

  • Chan W, Lam T, Ting H, Wong P (2004) New results on on-demand broadcasting with deadline via job scheduling with cancellation. Comput Comb 3106:210–218

    MathSciNet  Google Scholar 

  • Chin F, Fung S (2003) Online scheduling with partial job values: does timesharing or randomization help? Algorithmica 37(3):149–164

    Article  MATH  MathSciNet  Google Scholar 

  • Chrobak M, Jawor W, Sgall J, Tichỳ T (2004) Improved online algorithms for buffer management in qos switches. Algorithms-ESA 3221:204–215

    Google Scholar 

  • Cole R, Dobzinski S, Fleischer L (2008) Prompt mechanisms for online auctions. Algorithmic Game Theory 4997:170–181

  • Dósa G, Epstein L (2010) Online scheduling with a buffer on related machines. J comb optim 20(2):161–179

    Article  MATH  MathSciNet  Google Scholar 

  • Edelman B, Ostrovsky M, Schwarz M (2007) Internet advertising and the generalized second-price auction: selling billions of dollars worth of keywords. Am Econ Rev 97(1):242–259

    Article  Google Scholar 

  • Englert M, Westermann M (2007) Considering suppressed packets improves buffer management in qos switches. In Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, 209–218

  • Li R, Yang L, He X, Chen Q, Cheng X (2011) Semi-online scheduling for jobs with release times. J Comb Optim, 1–17

  • Nisan N, Bayer J, Chandra D, Franji T, Gardner R, Matias Y, Rhodes N, Seltzer M, Tom D, Varian H et al (2009) Google’s auction for tv ads. Autom, Lang Program, 309–327

  • Ting H (2006) A near optimal scheduler for on-demand data broadcasts. Algorithms Complex 3998:163–174

    Article  Google Scholar 

  • Ting H, Xiang X (2012) Equilibria of gsp for range auction. In: Gudmundsson J, Mestre J, Viglas A (eds) Computing and combinatorics. Springer, New York, pp 580–591

  • Vickrey W (1961) Counterspeculation, auctions, and competitive sealed tenders. J Financ 16(1):8–37

    Article  Google Scholar 

  • Zhou Y, Chakrabarty D, Lukose R (2008) Budget constrained bidding in keyword auctions and online knapsack problems. Internet Netw Econ 5385:566–576

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong, China

    Xiangzhong Xiang

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  1. Xiangzhong Xiang
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Correspondence to Xiangzhong Xiang.

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A preliminary version appeared in COCOA’2013.

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Xiang, X. Prompt mechanism for online auctions with multi-unit demands. J Comb Optim 30, 335–346 (2015). https://doi.org/10.1007/s10878-014-9754-9

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  • DOI: https://doi.org/10.1007/s10878-014-9754-9

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