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A Note on Revenue Maximization and Efficiency in Multi-Object Auctions

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  • Jehiel, Phillipe

    ()
    (ENPC, CERAS, Paris and UCL, London)

  • Moldovanu, Benny

    ()
    (Department of Economics, University of Mannheim, Germany)

Abstract

We consider an auction with risk neutral agents having independent private valuations for several heterogenous objects. Most of the literature on revenue-maximizing auctions has focused on the sale of one good or on the sale of several identical units (thus yielding one-dimensional informational models). Two reasons for inefficiency in revenue-maximizing auctions have been identified 1) The (monopolist) seller can increase revenue by restricting supply. 2) A revenue maximizing seller will sell to bidders with the highest ''virtual'' valuations (see Myerson, 1981). Virtual valuations are adjusted valuations that take into account bidders' informational rents, and depend on the distribution of private information. Asymmetries among bidders (and possibly other properties of these distributions) drive a wedge between virtual and true valuations, leading to inefficiencies (see Ausubel and Cramton, 1998 for a recent discussion of these issues). Our purpose here is to illustrate in the simplest possible way that a revenue-maximizing seller of several heterogenous objects has incentives to ''misallocate'' the sold objects even in symmetric settings, and no matter what the (symmetric) function governing the distribution of private information is. This inefficiency result should be contrasted with the efficiency result in Armstrong (1998) that applies only to some cases with discrete distributions of valuations.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 99-73.

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Length: 4 pages
Date of creation: 15 May 1999
Date of revision:
Handle: RePEc:xrs:sfbmaa:99-73

Note: Financial Support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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  1. Armstrong, Mark, 2000. "Optimal Multi-object Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 455-81, July.
  2. Engelbrecht-Wiggans, Richard, 1988. "Revenue equivalence in multi-object auctions," Economics Letters, Elsevier, vol. 26(1), pages 15-19.
  3. Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
  4. repec:wop:humbsf:2000-72 is not listed on IDEAS
  5. Page Jr., F.H., 1997. "Existence of Optimal Auctions in General Environments," Discussion Paper 1997-28, Tilburg University, Center for Economic Research.
  6. Lawrence M. Ausubel & Peter Cramton, 1998. "The Optimality of Being Efficient," Papers of Peter Cramton 98wpoe, University of Maryland, Department of Economics - Peter Cramton, revised 18 Jun 1999.
  7. Palfrey, Thomas R, 1983. "Bundling Decisions by a Multiproduct Monopolist with Incomplete Information," Econometrica, Econometric Society, vol. 51(2), pages 463-83, March.
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Cited by:
  1. Rapisarda, G., 2004. "A note on low-price menu auctions," Economics Letters, Elsevier, vol. 83(3), pages 343-346, June.
  2. Sandro Brusco & Giuseppe Lopomo, 2002. "Collusion via Signalling in Simultaneous Ascending Bid Auctions with Heterogeneous Objects, with and without Complementarities," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 407-436.
  3. Nicolas Figueroa & Vasiliki Skreta, 2006. "The Role of Outside Options in Auction Design," Levine's Bibliography 321307000000000140, UCLA Department of Economics.
  4. Bresky, Michal, 2013. "Revenue and efficiency in multi-unit uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 82(C), pages 205-217.
  5. Jackson, Matthew O. & Kremer, Ilan, 2004. "The relationship between the allocation of goods and a seller's revenue," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 371-392, June.

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