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Algorithmica

, Volume 77, Issue 1, pp 1–15 | Cite as

Revenue and Reserve Prices in a Probabilistic Single Item Auction

  • Noga Alon
  • Moran FeldmanEmail author
  • Moshe Tennenholtz
Article
  • 193 Downloads

Abstract

We investigate the effect of limiting the number of reserve prices on the revenue in a probabilistic single item auction. In the model considered, bidders compete for an impression drawn from a known distribution of possible types. The auction mechanism sets up to \(\ell \) reserve prices, and each impression type is assigned the highest reserve price lower than the valuation of some bidder for it. The bidder proposing the highest bid for an arriving impression gets it provided his bid is at least the corresponding reserve price, and pays the maximum between the reserve price and the second highest bid. Since the number of impression types may be huge, we consider the revenue \(R_{\ell }\) that can be ensured using only \(\ell \) reserve prices. Our main results are tight lower bounds on \(R_{\ell }\) for the cases where the impressions are drawn from the uniform or a general probability distribution.

Keywords

Reserve prices Second price auctions Single item auctions Revenue maximization 

Mathematics Subject Classification

91B26 91A28 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Microsoft ResearchHerzliyaIsrael
  2. 2.Tel Aviv UniversityTel AvivIsrael
  3. 3.EPFLLausanneSwitzerland
  4. 4.Technion-IITHaifaIsrael

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