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The multiple unit auction with variable supply

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Author Info
Yvan Lengwiler

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Abstract

The theory of multiple unit auctions traditionally assumes that the offered quantity is fixed. I argue that this assumption is not appropriate for many applications because the seller may be able and willing to adjust the supply to the bidding. In this paper I address this shortcoming by analyzing a multi-unit auction game between a monopolistic seller who can produce arbitrary quantities at constant unit cost, and oligopolistic bidders. I establish the existence of a subgame-perfect equilibrium for price discriminating and for uniform price auctions. I also show that bidders have an incentive to misreport their true demand in both auction formats, but they do that in different ways and for different reasons. Furthermore, both auction formats are inefficient, but there is no unambiguous ordering among them. Finally, the more competitive the bidders are, the more likely the seller is to prefer uniform pricing over price discrimination, yet increased competition among bidders may or may not enhance efficiency.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1998-28.

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Date of creation: 1998
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Handle: RePEc:fip:fedgfe:1998-28

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Keywords: Auctions ; Supply and demand;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Menezes, Flavio M. & Monteiro, Paulo K., 1995. "Existence of equilibrium in a discriminatory price auction," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 285-292, December. [Downloadable!] (restricted)
    Other versions:
  2. Nautz, D., 1995. "Optimal bidding in multi-unit auctions with many bidders," Economics Letters, Elsevier, vol. 48(3-4), pages 301-306, June. [Downloadable!] (restricted)
  3. Tenorio, Rafael, 1997. "On Strategic Quantity Bidding in Multiple Unit Auctions," Journal of Industrial Economics, Blackwell Publishing, vol. 45(2), pages 207-17, June. [Downloadable!] (restricted)
  4. Robert G. Hansen, 1988. "Auctions with Endogenous Quantity," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 44-58, Spring. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. 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.
  7. Lawrence M. Ausubel & Peter Cramton, 1995. "Demand Reduction and Inefficiency in Multi-Unit Auctions," Papers of Peter Cramton 98wpdr, University of Maryland, Department of Economics - Peter Cramton, revised 22 Jul 2002. [Downloadable!]
  8. Hans Haller & Yvan Lengwiler, 1998. "A discrete model of discriminatory price auctions - an alternative to Menezes-Monteiro," Finance and Economics Discussion Series 1998-08, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  9. Back, Kerry & Zender, Jaime F, 1993. "Auctions of Divisible Goods: On the Rationale for the Treasury Experiment," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(4), pages 733-64. [Downloadable!] (restricted)
  10. Nautz, D. & Wolfstetter, E., 1997. "Bid shading and risk aversion in multi-unit auctions with many bidders," Economics Letters, Elsevier, vol. 56(2), pages 195-200, October. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Damian S. Damianov, 2006. "Auctions with Endogenous Supply and the Walrasian Outcome," Keele Economics Research Papers KERP 2006/12, Centre for Economic Research, Keele University. [Downloadable!]
  2. Rocholl, Jörg, 2005. "Discriminatory auctions with seller discretion : evidence from German treasury auctions," Discussion Paper Series 1: Economic Studies 2005,15, Deutsche Bundesbank, Research Centre. [Downloadable!]
  3. Houssein Ben-Ameur & Brahim Chaib-draa & Peter Kropf, 2002. "Multi-item Auctions for Automatic Negotiation," CIRANO Working Papers 2002s-68, CIRANO. [Downloadable!]
  4. Marco LiCalzi & Alessandro Pavan, 2002. "Tilting the Supply Schedule to Enhance Competition in Uniform- Price Auctions," Game Theory and Information 0210003, EconWPA. [Downloadable!]
    Other versions:
  5. Keunkwan Ryu & Gyung-Rok Kim & Seonghwan Oh, 2004. "Discriminatory vs Uniform Price Auction: Auction Revenue," Econometric Society 2004 Far Eastern Meetings 539, Econometric Society. [Downloadable!]
  6. Lawrence M. Ausubel & Peter Cramton, 2004. "Vickrey Auctions with Reserve Pricing," Papers of Peter Cramton 99wpvic, University of Maryland, Department of Economics - Peter Cramton, revised 28 Jun 1999. [Downloadable!]
    Other versions:
  7. Skully, David W., 1999. "The Economics Of Trq Administration," Working Papers 14584, International Agricultural Trade Research Consortium. [Downloadable!]
  8. Sara Castellanos, 2001. "A New Empirical Study of the Mexican Treasury Securities Primary Auctions: Is there more underpricing?," Levine's Working Paper Archive 625018000000000206, David K. Levine. [Downloadable!]
  9. Christian Ewerhart & Nuno Cassola & Natacha Valla, 2006. "Declining valuations and equilibrium bidding in central bank refinancing operations," Working Paper Series 668, European Central Bank. [Downloadable!]
    Other versions:
  10. Sara Castellanos, 2001. "Mexican treasury securities primary auctions," Theory workshop papers 357966000000000025, UCLA Department of Economics. [Downloadable!]
  11. Christian Ewerhart & Nuno Cassola & Natacha Valla, 2005. "Equilibrium and inefficiency in fixed rate tenders," Working Paper Series 554, European Central Bank. [Downloadable!]
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