Optimal Auction in a Multidimensional World
A long-standing unsolved problem, often arising from auctions with multidimensional bids, is how to design seller-optimal auctions when bidders' private characteristics ("types") differ in many dimensions. This paper solves the problem, assuming bidder-types stochastically independent across bidders. First, it proves that in any optimal auction, with positive probability, the object is not sold. Thus, a standard auction without a reserve price is not optimal. Second, and more importantly, the paper obtains an explicit formula for optimal auctions in a class of environments. The optimal mechanism is almost equivalent to a Vickrey auction with reserve price, except that the bids are ranked by an optimal scoring rule, which assigns scores to the multidimensional bids. When the hazard rate of a statistic of bidder-types is monotone, this auction is optimal among all "scoring mechanisms," where a winner chooses a multidimensional payment bundle subject to a type-specific rule. Our optimal auction implies that an optimizing seller would not evaluate bid by her own preferences; instead, she would induce downward distortion of nonmonetary provisions from the first-best configuration. Applied to multidimensional nonlinear pricing, our design of optimal auction yields an explicit optimal pricing function.
|Date of creation:||Jan 2000|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.kellogg.northwestern.edu/research/math/Email:
More information through EDIRC
|Order Information:|| Email: |
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.:
- Jehiel, Phillipe & Moldovanu, Benny & Stacchetti, E., 1997.
"Multidimensional Mechanism Design for Auctions with Externalities,"
Sonderforschungsbereich 504 Publications
97-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
- 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.
- Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
- Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
- Babcock, Bruce A. & Lakshminarayan, P. G. & Wu, J. & Zilberman, David, 1997. "Targeting Tools for the Purchase of Environmental Amenities," Staff General Research Papers 5220, Iowa State University, Department of Economics.
- Laffont, Jean-Jacques & Tirole, Jean, 1987.
"Auctioning Incentive Contracts,"
Journal of Political Economy,
University of Chicago Press, vol. 95(5), pages 921-37, October.
- Chao, Hung-Po & Wilson, Robert, 2002. "Multi-dimensional Procurement Auctions for Power Reserves: Robust Incentive-Compatible Scoring and Settlement Rules," Journal of Regulatory Economics, Springer, vol. 22(2), pages 161-83, September.
- Yeon-Koo Che, 1993.
"Design Competition through Multidimensional Auctions,"
RAND Journal of Economics,
The RAND Corporation, vol. 24(4), pages 668-680, Winter.
- Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
- David Zilberman, 1996. "The Economics of a Public Fund for Environmental Amenities: A Study of CRP Contracts," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(4), pages 961-971.
- Babcock, Bruce A. & Lakshminarayan, P. G. & Wu, JunJie & Zilberman, David, 1996. "Economics of a Public Fund for Environmental Amenities (The)," Staff General Research Papers 1065, Iowa State University, Department of Economics.
- Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
- Armstrong, Mark, 2000. "Optimal Multi-object Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 455-81, July.
- Roger B. Myerson, 1988. "Mechanism Design," Discussion Papers 796, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Steven A. Matthews, 1995. "A Technical Primer on Auction Theory I: Independent Private Values," Discussion Papers 1096, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:1282. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fran Walker)
If references are entirely missing, you can add them using this form.