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 differ in many dimensions. This paper partially solves the problem in an auction setting with characteristics stochastically independent across bidders. The solution applies to the multidimensional versions of incentive contracts (Laffont and Tirole (1987) and Che (1993)) and nonlinear pricing (Armstrong (1996)). First, the paper proves that the multidimensionality requires that an optimal auction exclude a positive measure of bidders. Consequently, a standard auction without a reserve price or entrance fee is not optimal. Second, the paper obtains an explicit formula for optimal mechanisms, adopting the assumption of multiplicative separability from Armstrong (1996). Our optimal mechanism is almost equivalent to a Vickrey auction with a reserve price, except that the bids are ranked by an optimal scoring rule, which assigns scores to the multidimensional bids. This ``scoring-rule auction'' is optimal among all mechanisms if incentive compatibility constraints are non-binding (guaranteed by a hazard-rate assumption), and it is optimal among a smaller class of mechanisms if the constraints are binding. Our solution implies that an optimizing seller would induce downward distortion of a bid's nonmonetary provisions from the first-best configuration. Applied to multidimensional nonlinear pricing, our solution yields an explicit optimal pricing function.
|Date of creation:||01 Aug 2000|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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.:
- 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.
- McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
- Babcock, Bruce A. & Lakshminarayan, P. G. & Wu, J. & Zilberman, David, 1997. "Targeting Tools for the Purchase of Environmental Amenities," Staff General Research Papers Archive 5220, Iowa State University, Department of Economics.
- Babcock, Bruce A. & Lakshminarayan, P. G. & Wu, JunJie & Zilberman, David, 1996. "Economics of a Public Fund for Environmental Amenities (The)," Staff General Research Papers Archive 1065, Iowa State University, Department of Economics.
- 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.
- Che, Y.K., 1991.
"Design Competition through Multidimensional Auctions,"
9123, Wisconsin Madison - Social Systems.
- Yeon-Koo Che, 1993. "Design Competition through Multidimensional Auctions," RAND Journal of Economics, The RAND Corporation, vol. 24(4), pages 668-680, Winter.
- Moldovanu, Benny & Jehiel, Philippe & Stacchetti, Ennio, 1997.
"Multidimensional Mechanism Design for Auctions with Externalities,"
97-04, Sonderforschungsbreich 504.
- 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.
- 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.
- Jean-Jaques Laffont & Jean Tirole, 1985.
"Auctioning Incentive Contracts,"
403, Massachusetts Institute of Technology (MIT), 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.
- Mark Armstrong, 2000. "Optimal Multi-Object Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 455-481.
- Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Katherine Reichelderfer & William G. Boggess, 1988. "Government Decision Making and Program Performance: The Case of the Conservation Reserve Program," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 70(1), pages 1-11.
- Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
- Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
- 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:ecm:wc2000:0296. 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: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.