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

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  • Brett E Katzman

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    (Kennesaw State University)

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    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.

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    File URL: http://www.accessecon.com/Pubs/EB/2009/Volume29/EB-09-V29-I2-P33.pdf
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    Bibliographic Info

    Article provided by AccessEcon in its journal Economics Bulletin.

    Volume (Year): 29 (2009)
    Issue (Month): 2 ()
    Pages: 834-846

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    Handle: RePEc:ebl:ecbull:eb-09-00014

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    Related research

    Keywords: multi-unit auction; asymptotic equilibrium; efficiency;

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    1. 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.
    2. Swinkels, Jeroen M, 1999. "Asymptotic Efficiency for Discriminatory Private Value Auctions," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 509-28, July.
    3. 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 1041-63, September.
    4. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
    5. Indranil Chakraborty & Richard Engelbrecht-Wiggans, 2005. "Asymptotic prices in uniform-price multi-unit auctions," Economic Theory, Springer, vol. 26(4), pages 983-987, November.
    6. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Noussair, Charles, 1995. "Equilibria in a Multi-object Uniform Price Sealed Bid Auction with Multi-unit Demands," Economic Theory, Springer, vol. 5(2), pages 337-51, March.
    8. 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.
    9. Richard Engelbrecht-Wiggans & Charles M. Kahn, 1998. "Multi-unit auctions with uniform prices," Economic Theory, Springer, vol. 12(2), pages 227-258.
    10. Black, Jane & De Meza, David, 1992. "Systematic Price Differences between Successive Auctions Are No Anomaly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(4), pages 607-28, Winter.
    11. 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.
    12. Swinkels, Jeroen M, 2001. "Efficiency of Large Private Value Auctions," Econometrica, Econometric Society, vol. 69(1), pages 37-68, January.
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