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Optimal Auction in a Multidimensional World

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  • Charles Z. Zheng

Abstract

A long-standing unsolved problem, often arising from auctions with multidimensional bids, is how to design seller-optimal auctions when bidders' private characteristics ("types") differ in many dimensions. This paper solves the problem, assuming bidder-types stochastically independent across bidders. First, it proves that in any optimal auction, with positive probability, the object is not sold. Thus, a standard auction without a reserve price is not optimal. Second, and more importantly, the paper obtains an explicit formula for optimal auctions in a class of environments. The optimal mechanism is almost equivalent to a Vickrey auction with reserve price, except that the bids are ranked by an optimal scoring rule, which assigns scores to the multidimensional bids. When the hazard rate of a statistic of bidder-types is monotone, this auction is optimal among all "scoring mechanisms," where a winner chooses a multidimensional payment bundle subject to a type-specific rule. Our optimal auction implies that an optimizing seller would not evaluate bid by her own preferences; instead, she would induce downward distortion of nonmonetary provisions from the first-best configuration. Applied to multidimensional nonlinear pricing, our design of optimal auction yields an explicit optimal pricing function.

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  • Charles Z. Zheng, 2000. "Optimal Auction in a Multidimensional World," Discussion Papers 1282, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1282
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    Cited by:

    1. Leonardo Rezende, 2009. "Biased procurement auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(1), pages 169-185, January.
    2. Lamping, Jennifer, 2008. "Ignorance Is Bliss: Matching in Auctions with an Uninformed Seller," MPRA Paper 24374, University Library of Munich, Germany.
    3. Lamping, Jennifer, 2007. "The Value of Information in Auctions with Default Risk," MPRA Paper 24375, University Library of Munich, Germany.
    4. Levin, Dan & Peck, James & Ye, Lixin, 2007. "Bad news can be good news: Early dropouts in an English auction with multi-dimensional signals," Economics Letters, Elsevier, vol. 95(3), pages 462-467, June.
    5. Lamping, Jennifer, 2008. "The Value of Commitment in Auctions with Matching," MPRA Paper 24373, University Library of Munich, Germany.
    6. Fuqiang Zhang, 2010. "Procurement Mechanism Design in a Two-Echelon Inventory System with Price-Sensitive Demand," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 608-626, August.

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