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Asymptotic prices in uniform-price multi-unit auctions

Author

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  • Indranil Chakraborty
  • Richard Engelbrecht-Wiggans

Abstract

This paper considers a uniform-price auction in which each of n symmetric bidders can place, say, M bids. Each bidder has privately known, decreasing marginal values from an arbitrary M -dimensional distribution. We provide a quantile-type description of the asymptotic price that appropriately generalizes the characterization of the unit-demand asymptotic price. Specifically, the limiting price equals the $ (1-\alpha )$ -th quantile of the “average” of the marginal distributions if a fraction $\alpha $ of the demand is met asymptotically. The result also implies that the expected price in the limit as n becomes large depends only on the aggregate of the marginal distributions of each bidder’s marginal values (and not on the correlation between the marginal values). Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Indranil Chakraborty & Richard Engelbrecht-Wiggans, 2005. "Asymptotic prices in uniform-price multi-unit auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 983-987, November.
    • Handle: RePEc:spr:joecth:v:26:y:2005:i:4:p:983-987
    DOI: 10.1007/s00199-004-0549-6
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    Citations

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    Cited by:

    1. Ginsburgh, V. & van Ours, J.C., 2003. "How to Organize Sequential Auctions : Results of a Natural Experiment by Christie's," Other publications TiSEM 01ec6d80-7501-441c-a60b-c, Tilburg University, School of Economics and Management.
    2. Michal Bresky, 2008. "Properties of Equilibrium Strategies in Multiple-Unit, Uniform-Price Auctions," CERGE-EI Working Papers wp354, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    3. Congjun Rao & Yong Zhao & Junjun Zheng & Mark Goh & Cheng Wang, 2017. "Bidding Behavior and Equilibrium Excursion of Uniform Price Auction Mechanism," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-17, December.
    4. Chen, Ning & Ghosh, Arpita & Lambert, Nicolas S., 2014. "Auctions for social lending: A theoretical analysis," Games and Economic Behavior, Elsevier, vol. 86(C), pages 367-391.
    5. Brett E Katzman, 2009. "Asymptotic properties of equilibrium in discriminatory and uniform price ipv multi-unit auctions," Economics Bulletin, AccessEcon, vol. 29(2), pages 834-846.
    6. Chakraborty, Indranil & Shyamalkumar, Nariankadu D., 2014. "Revenue and efficiency ranking in large multi-unit and bundle auctions," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 12-21.

    More about this item

    Keywords

    Multi-unit auctions; Uniform price.;

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