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Abstract

A crucial assumption in the optimal auction literature is that each bidder's valuation is known to be drawn from a unique distribution. In this paper we study the optimal auction problem allowing for ambiguity about the distribution of valuations. Agents may be ambiguity averse (modeled using the maxmin expected utility model of Gilboa and Schmeidler 1989.) When the bidders face more ambiguity than the seller we show that (i) given any auction, the seller can always (weakly) increase revenue by switching to an auction providing full insurance to all types of bidders, (ii) if the seller is ambiguity neutral and any prior that is close enough to the seller's prior is included in the bidders' set of priors then the optimal auction is a full insurance auction, and (iii) in general neither the first nor the second price auction is optimal (even with suitably chosen reserve prices). When the seller is ambiguity averse and the bidders are ambiguity neutral an auction that fully insures the seller is in the set of optimal mechanisms.

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File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20060411/946/39
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Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 1 (2006)
Issue (Month): 4 (December)
Pages: 411-438

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Handle: RePEc:the:publsh:203

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Web page: http://econtheory.org

Related research

Keywords: Auctions; mechanism design; ambiguity; uncertainty;

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Find related papers by JEL classification:

• D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

References

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1. Karni, E. & Safra, Z., 1988. "Rank-Dependent Probabilities," Papers 11-88, Tel Aviv.
   
   • Karni, Edi & Safra, Zvi, 1990. "Rank-Dependent Probabilities," Economic Journal, Royal Economic Society, vol. 100(401), pages 487-95, June.
2. 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) halshs-00174553, HAL.
   
   • Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
   • Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie Mathématique et Applications 98.30, Université Panthéon-Sorbonne (Paris 1).
3. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-99, November.
4. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
5. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
   
   • Steven A. Matthews, 1981. "Selling to Risk Averse Buyers with Unobservable Tastes," Discussion Papers 480S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
6. Eso, Peter & Futo, Gabor, 1999. "Auction design with a risk averse seller," Economics Letters, Elsevier, vol. 65(1), pages 71-74, October.
7. Volij, Oscar, 2002. "Payoff equivalence in sealed bid auctions and the dual theory of choice under risk," Economics Letters, Elsevier, vol. 76(2), pages 231-237, July.
8. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-31, December.
   
   • 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.
9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
10. Karni, Edi & Safra, Zvi, 1989. "Dynamic Consistency, Revelations in Auctions and the Structure of Preferences," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 421-33, July.
11. Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
12. Volij, Oscar, 2002. "Payoff Equivalence in Sealed Bid Auctions and the Dual Theory of Choice Under Risk," Staff General Research Papers 10129, Iowa State University, Department of Economics.
13. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
    
    • Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.

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