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Asymptotic properties of equilibrium in discriminatory and uniform price ipv multi-unit auctions

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  • Brett E Katzman

    () (Kennesaw State University)

Abstract

This paper confronts the tractability problems that accompany IPV auction models with multi-unit bidder demands. Utilizing a first order approach, the asymptotic properties of symmetric equilibria in discriminatory and uniform price auctions are derived. It is shown that as the number of bidders increases, equilibrium bids converge to valuations in both discriminatory auctions and uniform price auctions where the price paid is determined by the lowest winning bid, thus indicating that the limiting case of these auctions correspond to price taking as in neoclassical models of consumer behavior. However, when the uniform price paid is tied to the highest losing bid, price taking behavior does not ensue and ex post inefficient allocations ares possible. The impact of our results on analysis of k-double auctions with multi-unit bidders demands is also discussed.

Suggested Citation

  • 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.
  • Handle: RePEc:ebl:ecbull:eb-09-00014
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    File URL: http://www.accessecon.com/Pubs/EB/2009/Volume29/EB-09-V29-I2-P33.pdf
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    References listed on IDEAS

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    1. Jane Black & David de Meza, 1992. "Systematic Price Differences Between Successive Auctionsare no Anomaly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(4), pages 607-628, December.
    2. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    3. Jeroen M. Swinkels, 1999. "Asymptotic Efficiency for Discriminatory Private Value Auctions," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 509-528.
    4. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1998. "Multi-Unit Pay-Your-Bid Auctions with Variable Awards," Games and Economic Behavior, Elsevier, vol. 23(1), pages 25-42, April.
    5. Richard Engelbrecht-Wiggans & Charles M. Kahn, 1998. "Multi-unit auctions with uniform prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 227-258.
    6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    7. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    8. Swinkels, Jeroen M, 2001. "Efficiency of Large Private Value Auctions," Econometrica, Econometric Society, vol. 69(1), pages 37-68, January.
    9. 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.
    10. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    11. V. V. Chari & Robert J. Weber, 1992. "How the U.S. Treasury should auction its debt," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 3-12.
    12. 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. 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.

    More about this item

    Keywords

    multi-unit auction; asymptotic equilibrium; efficiency;

    JEL classification:

    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D0 - Microeconomics - - General

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