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

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  • Francisco Alvarez

  • Cristina Mazón

Abstract

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

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    1. Michael B. Gordy, "undated". "Multiple Bids in a Multiple-Unit Common Value Auction," Computing in Economics and Finance 1996 _021, Society for Computational Economics.
    2. 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.
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    4. 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.
    5. 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.
    6. Lawrence M. Ausubel & Peter Cramton & Marek Pycia & Marzena Rostek & Marek Weretka, 2014. "Demand Reduction and Inefficiency in Multi-Unit Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1366-1400.
    7. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    8. 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.
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    Cited by:

    1. 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.
    2. Francisco Álvarez & Francisco André, 2015. "Auctioning Versus Grandfathering in Cap-and-Trade Systems with Market Power and Incomplete Information," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(4), pages 873-906, December.
    3. Alvarez, Francisco & André, Francisco J., 2015. "Auctioning emission permits in a leader-follower setting," MPRA Paper 61698, University Library of Munich, Germany.
    4. Francisco Alvarez & Cristina Mazón & Francisco Javier André, 2019. "Assigning pollution permits: are uniform auctions efficient?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 211-248, February.
    5. Alvarez, Francisco & André, Francisco J., 2013. "Auctioning vs. Grandfathering in Cap-and-Trade Systems with Market Power and Incomplete Information," Climate Change and Sustainable Development 162381, Fondazione Eni Enrico Mattei (FEEM).
    6. Alvarez Francisco & André Francisco J., 2016. "Auctioning Emission Permits with Market Power," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 16(4), pages 1-28, October.
    7. 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.

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    JEL classification:

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

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