On the Approximation Ratio of k-Lookahead Auction

  • Xue Chen
  • Guangda Hu
  • Pinyan Lu
  • Lei Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

Abstract

We consider the problem of designing a profit-maximizing single-item auction, where the valuations of bidders are correlated. We revisit the k-lookahead auction introduced by Ronen [6] and recently further developed by Dobzinski, Fu and Kleinberg [2]. By a more delicate analysis, we show that the k-lookahead auction can guarantee at least \(\frac{e^{1-1/k}}{e^{1-1/k}+1}\) of the optimal revenue, improving the previous best results of \(\frac{2k-1}{3k-1}\) in [2]. The 2-lookahead auction is of particular interest since it can be derandomized [2, 5]. Therefore, our result implies a polynomial time deterministic truthful mechanism with a ratio of \(\frac{\sqrt{e}}{\sqrt{e}+1}\) ≈ 0.622 for any single-item correlated-bids auction, improving the previous best ratio of 0.6. Interestingly, we can show that our analysis for 2-lookahead is tight. As a byproduct, a theoretical implication of our result is that the gap between the revenues of the optimal deterministically truthful and truthful-in-expectation mechanisms is at most a factor of \(\frac{1+\sqrt{e}}{\sqrt{e}}\). This improves the previous best factor of \(\frac{5}{3}\) in [2].

Keywords

Approximation Ratio Explicit Model Price Auction Expected Revenue Threshold Price 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cremer, J., McLean, R.P.: Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica 53(2), 345–361 (1985)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Dobzinski, S., Fu, H., Kleinberg, R.D.: Optimal auctions with correlated bidders are easy. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 129–138 (2011)Google Scholar
  3. 3.
    Klemperer, P.: Auction theory: A guide to the literature. Microeconomics, EconWPA (March 1999)Google Scholar
  4. 4.
    Myerson, R.B.: Optimal acution design. Mathematics of Operations Research 6(1), 58–73 (1981)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Papadimitriou, C.H., Pierrakos, G.: On optimal single-item auctions. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 119–128 (2011)Google Scholar
  6. 6.
    Ronen, A.: On approximating optimal auctions. In: Proceedings of the 3rd ACM Conference on Electronic Commerce, EC 2001, pp. 11–17 (2001)Google Scholar
  7. 7.
    Ronen, A., Saberi, A.: On the hardness of optimal auctions. In: Proceedings of the 43rd Symposium on Foundations of Computer Science, FOCS 2002, pp. 396–405 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xue Chen
    • 1
  • Guangda Hu
    • 2
  • Pinyan Lu
    • 3
  • Lei Wang
    • 4
  1. 1.Department of Computer ScienceUniversity of Texas at AustinUSA
  2. 2.Department of Computer SciencePrinceton UniversityUSA
  3. 3.Microsoft Research AsiaUSA
  4. 4.Georgia Institute of TechnologyUSA

Personalised recommendations