A Note on Revenue Maximization and Efficiency in Multi-Object Auctions
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.
|Date of creation:||15 May 1999|
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- 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.
- Armstrong, Mark, 2000. "Optimal Multi-object Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 455-81, July.
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- 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.
- Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
- Paul Milgrom, . "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Working Papers 98002, Stanford University, Department of Economics.
- Page Jr., Frank H., 1998.
"Existence of optimal auctions in general environments,"
Journal of Mathematical Economics,
Elsevier, vol. 29(4), pages 389-418, May.
- Page Jr., F.H., 1997. "Existence of Optimal Auctions in General Environments," Discussion Paper 1997-28, Tilburg University, Center for Economic Research.
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