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Lower Bounds on Revenue of Approximately Optimal Auctions

  • Balasubramanian Sivan
  • Vasilis Syrgkanis
  • Omer Tamuz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers’ valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Specifically, we show that a single price drawn from the distribution of the maximum valuation v max = max{V 1,V 2,…,V n } achieves a revenue of at least a \(\frac{1}{e}\) fraction of the geometric expectation of v max. This generic bound is a measure of how revenue improves/degrades as a function of the concentration/spread of v max.

We further show that in absence of buyers’ valuation distributions, recruiting an additional set of identical bidders will yield a similar guarantee on revenue. Finally, our bound also gives a measure of the extent to which one can simultaneously approximate welfare and revenue in terms of the concentration/spread of v max.

Keywords

Revenue Auction Geometric expectation Single posted price 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Balasubramanian Sivan
    • 1
  • Vasilis Syrgkanis
    • 2
  • Omer Tamuz
    • 3
  1. 1.Computer Sciences Dept.University of Winsconsin-MadisonUSA
  2. 2.Dept. of Computer ScienceCornell UniversityIthacaUSA
  3. 3.Weizmann InstituteRehovotIsrael

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