Optimal auctions with ambiguity
A crucial assumption in the optimal auction literature has been that each bidder's valuation is known to be drawn from a single unique distribution. In this paper we relax this assumption and study the optimal auction problem when there is ambiguity about the distribution from which these valuations are drawn and where the seller or the bidder may display ambiguity aversion. We model ambiguity aversion using the maxmin expected utility model where an agent evaluates an action on the basis of the minimum expected utility over the set of priors, and then chooses the best action amongst them. We first consider the case where the bidders are ambiguity averse (and the seller is ambiguity neutral). Our first result shows that the optimal incentive compatible and individually rational mechanism must be such that for each type of bidder the minimum expected utility is attained by using the seller's prior. Using this result we show that an auction that provides full insurance to all types of bidders is always in the set of optimal auctions. In particular, when the bidders' set of priors is the Îµ- contamination of the seller's prior the unique optimal auction provides full insurance to bidders of all types. We also show that in general, many classical auctions, including first and second price are not the optimal mechanism (even with suitably chosen reserve prices). We next consider the case when the seller is ambiguity averse (and the bidders are ambiguity neutral). Now, the optimal auction involves the seller being perfectly insured. Hence, as long as bidders are risk and ambiguity neutral, ambiguity aversion on the part of the seller seems to play a similar role to that of risk aversion.
|Date of creation:||11 Aug 2004|
|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
References listed on IDEAS
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.:
- Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-99, November.
- Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000.
"Sharing beliefs: between agreeing and disagreeing,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Itzhak Gilboa & Antoine Billot & Alain Chateauneuf & Jean-Marc Tallon, 2000. "Sharing Beliefs: between Agreeing and Disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00753122, HAL.
- Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie MathÃ©matique et Applications 98.30, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- J. Riley & E. Maskin, 1981.
"Optimal Auctions with Risk Averse Buyers,"
311, Massachusetts Institute of Technology (MIT), Department of Economics.
- Volij, Oscar, 2002.
"Payoff equivalence in sealed bid auctions and the dual theory of choice under risk,"
Elsevier, vol. 76(2), pages 231-237, July.
- Volij, Oscar, 2002. "Payoff Equivalence in Sealed Bid Auctions and the Dual Theory of Choice Under Risk," Staff General Research Papers Archive 10129, Iowa State University, Department of Economics.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Steven A. Matthews, 1981.
"Selling to Risk Averse Buyers with Unobservable Tastes,"
480S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
- Mukerji, S., 1997.
"Ambiguity aversion and incompleteness of contractual form,"
Discussion Paper Series In Economics And Econometrics
9715, Economics Division, School of Social Sciences, University of Southampton.
- Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-31, December.
- Karni, Edi & Safra, Zvi, 1990.
Royal Economic Society, vol. 100(401), pages 487-95, June.
- Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
- Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
- Eso, Peter & Futo, Gabor, 1999. "Auction design with a risk averse seller," Economics Letters, Elsevier, vol. 65(1), pages 71-74, October.
- Edi Karni & Zvi Safra, 1989. "Dynamic Consistency, Revelations in Auctions and the Structure of Preferences," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 421-433.
When requesting a correction, please mention this item's handle: RePEc:ecm:nasm04:609. 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.