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].

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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

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