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Optimal auctions with ambiguity

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  • Andreas Pape
  • Subir Bose
  • Emre Ozdenoren

Abstract

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 ε- 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.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 609.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:609

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Keywords: Optimal auction; mechanism design; ambiguity; uncertainty;

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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  2. 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.
  3. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-99, November.
  4. Karni, E. & Safra, Z., 1988. "Rank-Dependent Probabilities," Papers 11-88, Tel Aviv.
  5. 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.
  6. 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.
  7. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  8. repec:hal:cesptp:halshs-00174553 is not listed on IDEAS
  9. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
  10. 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).
  11. Eso, Peter & Futo, Gabor, 1999. "Auction design with a risk averse seller," Economics Letters, Elsevier, vol. 65(1), pages 71-74, October.
  12. Karni, E. & Safra, Z., 1988. "Ascending Bid Auctions With Behaviorally Consistent Bidders," Papers 1-88, Tel Aviv.
  13. 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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