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Multi-unit auctions with private information: an indivisible unit continuous price model


  • Francisco Alvarez


  • Cristina Mazón



We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller’s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information. Copyright Springer-Verlag 2012

Suggested Citation

  • Francisco Alvarez & Cristina Mazón, 2012. "Multi-unit auctions with private information: an indivisible unit continuous price model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 35-70, September.
  • Handle: RePEc:spr:joecth:v:51:y:2012:i:1:p:35-70 DOI: 10.1007/s00199-010-0594-2

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    References listed on IDEAS

    1. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    2. Jaime F. Zender & James J.D. Wang, 2002. "Auctioning divisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 673-705.
    3. Brenner, Menachem & Galai, Dan & Sade, Orly, 2009. "Sovereign debt auctions: Uniform or discriminatory?," Journal of Monetary Economics, Elsevier, vol. 56(2), pages 267-274, March.
    4. Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 675-689.
    5. Indranil Chakraborty, 2006. "Characterization of equilibrium in pay-as-bid auctions for multiple units," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 197-211, September.
    6. Noussair, Charles, 1995. "Equilibria in a Multi-object Uniform Price Sealed Bid Auction with Multi-unit Demands," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 337-351, March.
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    Cited by:

    1. Francisco Alvarez & Francisco J. André, 2013. "Auctioning vs. Grandfathering in Cap-and-Trade Systems with Market Power and Incomplete Information," Working Papers 2013.98, Fondazione Eni Enrico Mattei.
    2. repec:wsi:apjorx:v:34:y:2017:i:06:n:s0217595917500282 is not listed on IDEAS
    3. Francisco Alvarez & Cristina Mazón, 2016. "Price volatility in the secondary market and bidders’ heterogeneous behavior in Spanish Treasury auctions," Empirical Economics, Springer, vol. 50(4), pages 1435-1466, June.
    4. Alvarez, Francisco & André, Francisco J., 2015. "Auctioning emission permits in a leader-follower setting," MPRA Paper 61698, University Library of Munich, Germany.

    More about this item


    Multi-unit auctions; Indivisible good auctions; Treasury auctions; D44;

    JEL classification:

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


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