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Competitive Auction

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 186 Accesses

Years and Authors of Summarized Original Work

  • 2001; Goldberg, Hartline, Wright

  • 2002; Fiat, Goldberg, Hartline, Karlin

Problem Definition

This problem studies the one round, sealed-bid auction model where an auctioneer would like to sell an idiosyncratic commodity with unlimited copies to n bidders and each bidder \(i \in \{ 1,\ldots ,n\}\) will get at most one item.

First, for any i, bidder i bids a value b i representing the price he is willing to pay for the item. They submit the bids simultaneously. After receiving the bidding vector \(\mathbf{b} = (b_{1},\ldots ,b_{n})\), the auctioneer computes and outputs the allocation vector \(\mathbf{x} = (x_{1},\ldots ,x_{n}) \in \{ 0,1\}^{n}\) and the price vector \(\mathbf{p} = (p_{1},\ldots ,p_{n})\). If for any i, x i  = 1, then bidder i gets the item and pays p i for it. Otherwise, bidder i loses and pays nothing. In the auction, the auctioneer’s revenue is \(\sum _{i=1}^{n}\mathbf{x}\mathbf{p}^{T}\).

Definition 1 (Optimal Single Price...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Software Engineering Institute, East China Normal University, Shanghai, China

    Tian-Ming Bu

Authors
  1. Tian-Ming Bu
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Correspondence to Tian-Ming Bu .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Bu, TM. (2016). Competitive Auction. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_78

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