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Allocating multiple units

Author

Listed:
  • Kala Krishna

    (Department of Economics, Pennsylvania State University, PA 16802, USA, and NBER, USA)

  • Torben Tranæ s

    (Institute of Economics, CIE, and EPRU, University of Copenhagen, 1455 Copenhagen, DENMARK)

Abstract

This paper studies the allocation and rent distribution in multi-unit, combinatorial-bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points.

Suggested Citation

  • Kala Krishna & Torben Tranæ s, 2002. "Allocating multiple units," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 733-750.
    • Handle: RePEc:spr:joecth:v:20:y:2002:i:4:p:733-750
    Note: Received: December 23, 1999; revised version: December 10, 2001
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    Citations

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    Cited by:

    1. Chiesa, Gabriella & Denicolò, Vincenzo, 2009. "Trading with a common agent under complete information: A characterization of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 144(1), pages 296-311, January.
    2. Alcalde, José & Dahm, Matthias, 2008. "The Complete Information First. Price Auction or the Importance of Being Indivisible," Working Papers 2072/13264, Universitat Rovira i Virgili, Department of Economics.
    3. Elena Yusupova, 2006. "Information Asymmetry, Share Mispricing and the Coordination Problem: Investor Portfolio Choice in Czech Voucher Privatization," CERGE-EI Working Papers wp301, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    4. Bruno Larue & Sébastien Pouliot & Mohamed Jeddy, 2016. "On the Number and Heterogeneity of Bidders in Livestock Auctions," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 64(2), pages 289-310, June.
    5. José Alcalde & Matthias Dahm, 2011. "On The Complete Information First-Price Auction And Its Intuitive Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 353-361.

    More about this item

    Keywords

    Menu auctions; Multiple-unit auctions; First-price vs. second-price auctions; Revenue equivalence.;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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