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A note on revenue maximization and efficiency in multi-object auctions

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  • Jehiel, Philippe
  • Moldovanu, Benny

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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  • Jehiel, Philippe & Moldovanu, Benny, 1999. "A note on revenue maximization and efficiency in multi-object auctions," Papers 99-73, Sonderforschungsbreich 504.
    • Handle: RePEc:mnh:spaper:2839
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    References listed on IDEAS

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    1. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    2. 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.
    3. Steven R. Williams, 1994. "A Characterization of Efficient," Discussion Papers 1100, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Mark Armstrong, 2000. "Optimal Multi-Object Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 455-481.
    5. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
    6. Palfrey, Thomas R, 1983. "Bundling Decisions by a Multiproduct Monopolist with Incomplete Information," Econometrica, Econometric Society, vol. 51(2), pages 463-483, March.
    7. 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.
    8. Engelbrecht-Wiggans, Richard, 1988. "Revenue equivalence in multi-object auctions," Economics Letters, Elsevier, vol. 26(1), pages 15-19.
    9. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    Cited by:

    1. Nicolas Figueroa & Vasiliki Skreta, 2006. "The Role of Outside Options in Auction Design," Levine's Bibliography 321307000000000140, UCLA Department of Economics.
    2. Ari Hyytinen & Sofia Lundberg & Otto Toivanen, 2018. "Design of public procurement auctions: evidence from cleaning contracts," RAND Journal of Economics, RAND Corporation, vol. 49(2), pages 398-426, June.
    3. Rapisarda, G., 2004. "A note on low-price menu auctions," Economics Letters, Elsevier, vol. 83(3), pages 343-346, June.
    4. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2007. "Mixed bundling auctions," Journal of Economic Theory, Elsevier, vol. 134(1), pages 494-512, May.
    5. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 143-164, October.
    6. Jehiel, Philippe & Lamy, Laurent, 2014. "On discrimination in procurement auctions," CEPR Discussion Papers 9790, C.E.P.R. Discussion Papers.
    7. Sandro Brusco & Giuseppe Lopomo, 2004. "Collusion via Signalling in Simultaneous Ascending Bid Auctions with Heterogeneous Objects, with and without Complementarities," Levine's Bibliography 122247000000000385, UCLA Department of Economics.
    8. Peter Cramton & Andrzej Skrzypacz & Robert Wilson, 2007. "Revenues in the 700 MHz Spectrum Auction," Papers of Peter Cramton 07rev700, University of Maryland, Department of Economics - Peter Cramton, revised 2007.
    9. Bresky, Michal, 2013. "Revenue and efficiency in multi-unit uniform-price auctions," Games and Economic Behavior, Elsevier, vol. 82(C), pages 205-217.
    10. 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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