Sequential Posted Price Mechanisms with Correlated Valuations

  • Marek Adamczyk
  • Allan Borodin
  • Diodato Ferraioli
  • Bart de Keijzer
  • Stefano Leonardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)


We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a “take-it-or-leave-it” offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to the ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a \(\varOmega (1/\max \{1,d\})\) fraction of the optimal revenue can be extracted, where d denotes the “degree of dependence” of the valuations, ranging from complete independence (\(d=0\)) to arbitrary dependence (\(d = n-1\)). When we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i, we prove that a constant fraction \((2 - \sqrt{e})/4 \approx 0.088\) of the optimal revenue can be always extracted.



We thank Joanna Drummond, Brendan Lucier, Tim Roughgarden and anonymous referees for their constructive comments.


  1. 1.
    Adamczyk, M., Sviridenko, M., Ward, J.: Submodular stochastic probing on matroids. In: STACS 2014 (2014)Google Scholar
  2. 2.
    Adamczyk, M., Borodin, A., Ferraioli, D., de Keijzer, B., Leonardi, S.: Sequential posted price mechanisms with correlated valuations. CoRR, abs/1503.02200 (2015)Google Scholar
  3. 3.
    Babaioff, M., Dughmi, S., Kleinberg, R., Slivkins, A.: Dynamic pricing with limited supply. In: EC 2012 (2012)Google Scholar
  4. 4.
    Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: SODA 2007 (2007)Google Scholar
  5. 5.
    Babaioff, M., Immorlica, N., Lucier, B., Weinberg, S.M.: A simple and approximately optimal mechanism for an additive buyer. In: FOCS 2014 (2014)Google Scholar
  6. 6.
    Blum, A., Hartline, J.D.: Near-optimal online auctions. In: SODA 2005 (2005)Google Scholar
  7. 7.
    Blum, A., Kumar, V., Rudra, A., Wu, F.: Online learning in online auctions. Theor. Comput. Sci. 324, 137–146 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Blumrosen, L., Holenstein, T.: Posted prices vs. negotiations: an asymptotic analysis. In: EC 2008 (2008)Google Scholar
  9. 9.
    Börgers, T.: An Introduction to the Theory of Mechanism Design. Oxford University Press, Oxford (2015)Google Scholar
  10. 10.
    Chawla, S., Fu, H., Karlin, A.: Approximate revenue maximization in interdependent value settings. In: EC 2014, pp. 277–294 (2014)Google Scholar
  11. 11.
    Chawla, S., Hartline, J.D., Malec, D.L., Sivan, B.: Multi-parameter mechanism design and sequential posted pricing. In: STOC 2010 (2010)Google Scholar
  12. 12.
    Clarke, E.H.: Multipart pricing of public goods. Public Choice 11(1), 17–33 (1971)CrossRefGoogle Scholar
  13. 13.
    Cremer, J., McLean, R.P.: Full extraction of the surplus in bayesian and dominant strategy auctions. Econometrica 56(6), 1247–1257 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Devanur, N.R., Morgenstern, J., Syrgkanis, V., Weinberg, S.M.: Simple auctions with simple strategies. In: EC 2015, pp. 305–322 (2015)Google Scholar
  15. 15.
    Dobzinski, S., Fu, H., Kleinberg, R.D.: Optimal auctions with correlated bidders are easy. In: STOC 2011 (2011)Google Scholar
  16. 16.
    Feldman, M., Gravin, N., Lucier, B.: Combinatorial auctions via posted prices. In: SODA 2015 (2015)Google Scholar
  17. 17.
    Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gupta, A., Nagarajan, V.: A stochastic probing problem with applications. In: Goemans, M., Correa, J. (eds.) IPCO 2013. LNCS, vol. 7801, pp. 205–216. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  19. 19.
    Hart, S., Nisan, N.: Approximate revenue maximization with multiple items. In: EC 2012 (2012)Google Scholar
  20. 20.
    Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. SIGecom Exch. 8(1), 5:1–5:3 (2009)CrossRefGoogle Scholar
  21. 21.
    Kleinberg, R., Leighton, T.: The value of knowing a demand curve: bounds on regret for online posted-price auctions. In: FOCS 2003 (2003)Google Scholar
  22. 22.
    Kleinberg, R., Weinberg, S.M.: Matroid prophet inequalities. In: STOC 2012 (2012)Google Scholar
  23. 23.
    Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ronen, A.: On approximating optimal auctions. In: EC 2001 (2001)Google Scholar
  25. 25.
    Roughgarden, T., Talgam-Cohen, I.: Optimal and near-optimal mechanism design with interdependent values. In: EC 2013 (2013)Google Scholar
  26. 26.
    Rubinstein, A., Weinberg, S.M.: Simple mechanisms for a subadditive buyer and applications to revenue monotonicity. In: EC 2015, pp. 377–394 (2015)Google Scholar
  27. 27.
    Sandholm, T.W., Gilpin, A.: Sequences of take-it-or-leave-it offers: near-optimal auctions without full valuation revelation. In: Faratin, P., Parkes, D.C., Rodríguez-Aguilar, J.-A., Walsh, W.E. (eds.) AMEC 2003. LNCS (LNAI), vol. 3048, pp. 73–91. Springer, Heidelberg (2004) Google Scholar
  28. 28.
    Segal, I.: Optimal pricing mechanisms with unknown demand. Am. Econ. Rev. 93(3), 509–529 (2003)CrossRefGoogle Scholar
  29. 29.
    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Financ. 16(1), 8–37 (1961)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yan, Q.: Mechanism design via correlation gap. In: SODA 2011 (2011)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Marek Adamczyk
    • 1
  • Allan Borodin
    • 2
  • Diodato Ferraioli
    • 3
  • Bart de Keijzer
    • 1
  • Stefano Leonardi
    • 1
  1. 1.Sapienza University of RomeRomeItaly
  2. 2.University of TorontoTorontoCanada
  3. 3.University of SalernoFiscianoItaly

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