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Demand Reduction and Inefficiency in Multi-Unit Auctions

Abstract

Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multi-unit auctions. Large bidders reduce demand for additional units and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in several auction settings: flat demand and downward-sloping demand, independent private values and correlated values, and uniform pricing and pay-your-bid pricing. We also establish that the ranking of the uniform-price and pay-your-bid auctions is ambiguous. We show how a Vickrey auction avoids this inefficiency and how the Vickrey auction can be implemented with a simultaneous, ascending-bid design (Ausubel 1997). Bidding behavior in the FCC spectrum auctions illustrates the incentives for demand reduction and the associated inefficiency.

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File URL: http://www.cramton.umd.edu/papers1995-1999/98wp-demand-reduction.pdf
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Paper provided by University of Maryland, Department of Economics - Peter Cramton in its series Papers of Peter Cramton with number 98wpdr.

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Length: 31 pages
Date of creation: 08 Nov 1995
Date of revision: 22 Jul 2002
Handle: RePEc:pcc:pccumd:98wpdr
Note: Working Paper
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Economics Department, University of Maryland, College Park, MD 20742-7211

Phone: (202) 318-0520
Fax: (202) 318-0520
Web page: http://www.cramton.umd.edu

Keywords: Auctions; Multi-Unit Auctions; Spectrum Auctions; Treasury Auctions;

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Find related papers by JEL classification:
  • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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  1. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
  2. 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.
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  5. Ian Ayres & Peter Cramton, 1996. "Deficit Reduction Through Diversity: How Affirmative Action at the FCC Increased Auction Competition," Papers of Peter Cramton 96slr, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
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  8. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, Summer.
  9. James J. Anton & Dennis A. Yao, 1992. "Coordination in Split Award Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 681-707.
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  11. Harstad, Ronald M., 1993. "Auctions With Endogenous Bidder Participation," Discussion Paper Serie B 251, University of Bonn, Germany.
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  13. 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.
  14. Robert Wilson, 1979. "Auctions of Shares," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 675-689.
  15. Levin, Dan & Smith, James L, 1996. "Optimal Reservation Prices in Auctions," Economic Journal, Royal Economic Society, vol. 106(438), pages 1271-1283, September.
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  18. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  19. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
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  21. Engelbrecht-Wiggans, Richard, 1988. "Revenue equivalence in multi-object auctions," Economics Letters, Elsevier, vol. 26(1), pages 15-19.
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  23. Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
  24. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
  25. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
  26. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
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  28. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  29. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  30. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
  31. Lawrence M. Ausubel & Peter Cramton, 1997. "Auctioning Securities," Papers of Peter Cramton 98wpas, University of Maryland, Department of Economics - Peter Cramton, revised Mar 1998.
  32. 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.
  33. Back, Kerry & Zender, Jaime F, 1993. "Auctions of Divisible Goods: On the Rationale for the Treasury Experiment," Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 733-764.
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