Approximation Schemes for Sequential Posted Pricing in Multi-unit Auctions

  • Tanmoy Chakraborty
  • Eyal Even-Dar
  • Sudipto Guha
  • Yishay Mansour
  • S. Muthukrishnan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6484)

Abstract

We design algorithms for computing approximately revenue-maximizing sequential posted-pricing mechanisms (SPM) in K-unit auctions, in a standard Bayesian model. A seller has K copies of an item to sell, and there are n buyers, each interested in only one copy, and has some value for the item. The seller posts a price for each buyer, using Bayesian information about buyers’ valuations, who arrive in a sequence. An SPM specifies the ordering of buyers and the posted prices, and may be adaptive or non-adaptive in its behavior.

The goal is to design SPM in polynomial time to maximize expected revenue. We compare against the expected revenue of optimal SPM, and provide a polynomial time approximation scheme (PTAS) for both non-adaptive and adaptive SPMs. This is achieved by two algorithms: an efficient algorithm that gives a \((1-\frac{1}{\sqrt{2\pi K}})\)-approximation (and hence a PTAS for sufficiently large K), and another that is a PTAS for constant K. The first algorithm yields a non-adaptive SPM that yields its approximation guarantees against an optimal adaptive SPM – this implies that the adaptivity gap in SPMs vanishes as K becomes larger.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tanmoy Chakraborty
    • 1
  • Eyal Even-Dar
  • Sudipto Guha
    • 1
  • Yishay Mansour
    • 2
  • S. Muthukrishnan
    • 3
  1. 1.University of PennsylvaniaPhiladelphia
  2. 2.Google Israel and The Blavatnik School of Computer ScienceTel-Aviv UniversityTel-AvivIsrael
  3. 3.Google ResearchNew York

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