Approximately-strategyproof and tractable multiunit auctions

  • Authors:

  • Anshul Kothari;David C. Parkes;Subhash Suri

  • Affiliations:

  • Department of Computer Science, University of California at Santa Barbara, CA 93106, United States;Division of Engineering and Applied Sciences, 33 Oxford Street, Harvard University, Cambridge, MA 02138, United States;Department of Computer Science, University of California at Santa Barbara, CA 93106, United States

  • Venue:
  • Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
  • Year:
  • 2005

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Abstract

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multiunit allocation problem. The bidding language allows marginal-decreasing piecewise-constant curves and quantity-based side constraints. We develop a fully polynomial-time approximation scheme for the multiunit allocation problem, which computes a (1+@e) approximation in worst-case time T=O(n^3/@e), given n bids each with a constant number of pieces. We integrate this approximation scheme within a Vickrey-Clarke-Groves (VCG) mechanism and compute payments for an asymptotic cost of O(T log n). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by @eV/(1+@e), where V is the total surplus in the efficient outcome.