Learning Environmental Parameters for the Design of Optimal English Auctions with Discrete Bid Levels

  • A. Rogers
  • E. David
  • J. Schiff
  • S. Kraus
  • N. R. Jennings
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3937)


In this paper we consider the optimal design of English auctions with discrete bid levels. Such auctions are widely used in online internet settings and our aim is to automate their configuration in order that they generate the maximum revenue for the auctioneer. Specifically, we address the problem of estimating the values of the parameters necessary to perform this optimal auction design by observing the bidding in previous auctions. To this end, we derive a general expression that relates the expected revenue of the auction when discrete bid levels are implemented, but the number of participating bidders is unknown. We then use this result to show that the characteristics of these optimal bid levels are highly dependent on the expected number of bidders and on their valuation distribution. Finally, we derive and demonstrate an online algorithm based on Bayesian machine learning, that allows these unknown parameters to be estimated through observations of the closing price of previous auctions. We show experimentally that this algorithm converges rapidly toward the true parameter values and, in comparison with an auction using the more commonly implemented fixed bid increment, results in an increase in auction revenue.


Reserve Price Online Auction Closing Price English Auction Potential Bidder 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bajari, P., Hortacsu, A.: The winner’s curse, reserve prices, and endogenous entry: empirical insights from eBay auctions. RAND Journal of Economics 34(2), 329–355 (2003)CrossRefGoogle Scholar
  2. 2.
    Bichler, M., Kalagnanam, J.: A non-parametric estimator for setting reserve prices in procurement auctions. In: ACM Conference on Electronic Commerce 2003, pp. 254–255 (2003)Google Scholar
  3. 3.
    Chwe, M.S.-Y.: The discrete bid first auction. Economics Letters 31, 303–306 (1989)MathSciNetCrossRefGoogle Scholar
  4. 4.
    David, E., Rogers, A., Schiff, J., Kraus, S., Jennings, N.R.: Optimal design of english auctions with discrete bid levels. In: Proceedings of ACM Conference on Electronic Commerce, pp. 98–107 (2005)Google Scholar
  5. 5.
    Hageman, L.A., Young, D.M.: Applied Iterative Methods. Academic Press, London (1981)zbMATHGoogle Scholar
  6. 6.
    Laffont, J.-J., Ossard, H., Vuong, Q.: Econometrics of first-price auctions. Econometrica 63(4), 953–980 (1995)CrossRefzbMATHGoogle Scholar
  7. 7.
    Levin, D., Smith, J.L.: Equilibrium in auctions with entry. American Economic Review 84(3), 585–599 (1994)Google Scholar
  8. 8.
    Lucking-Reiley, D.H.: Auctions on the internet: What’s being auctioned, and how? Journal of Industrial Economics 48(3), 227–252 (2000)CrossRefGoogle Scholar
  9. 9.
    MacKay, D.J.C.: Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  10. 10.
    Myerson, R.: Optimal auction design. Mathematics of Operations Research 6(1), 58–73 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)zbMATHGoogle Scholar
  12. 12.
    Riley, J.G., Samuelson, W.F.: Optimal auctions. American Economic Review 71, 381–392 (1981)Google Scholar
  13. 13.
    Rothkopf, M.H., Harstad, R.: On the role of discrete bid levels in oral auctions. European Journal of Operations Research 74, 572–581 (1994)CrossRefzbMATHGoogle Scholar
  14. 14.
    Rothkopf, M.H., Teisberg, T.J., Kahn, E.P.: Why are Vickrey auctions rare? Journal of Political Economy 98(1), 94–109 (1990)CrossRefGoogle Scholar
  15. 15.
    Yamey, B.S.: Why 2,310,000 [pounds] for a Velazquez? An auction bidding rule. Journal of Political Economy 80, 1323–1327 (1972)CrossRefGoogle Scholar
  16. 16.
    Yu, J.: Discrete Approximation of Continous Allocation Mechanisms. PhD thesis, California Institute of Technology, Division of Humanities and Social Science (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • A. Rogers
    • 1
  • E. David
    • 1
  • J. Schiff
    • 2
  • S. Kraus
    • 3
  • N. R. Jennings
    • 1
  1. 1.Electronics and Computer ScienceUniversity of SouthamptonSouthamptonUK
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  3. 3.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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