Approximately-strategyproof and tractable multi-unit auctions

  • Authors:

  • Anshul Kothar;David C. Parke;Subhash Sur

  • Affiliations:

  • University of California at Santa Barbara, CA;Harvard University, Cambridge, MA;University of California at Santa Barbara, CA

  • Venue:
  • Proceedings of the 4th ACM conference on Electronic commerce
  • Year:
  • 2003

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Abstract

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language in our auctions allows marginal-decreasing piecewise constant curves. First, we develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a (1+ε)≈ in worst-case time T = O(n3/ε), given n bids each with a constant number of pieces. Second, we embed this approximation scheme within a Vickrey-Clarke-Groves (VCG) mechanism and compute payments to n agents 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 ε/(1+ε) V, where V is the total surplus in the efficient outcome.