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Risk aversion and optimal reserve prices in first- and second-price auctions

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  • Hu, Audrey
  • Matthews, Steven A.
  • Zou, Liang

Abstract

We analyze the effects of buyer and seller risk aversion in first- and second-price auctions in the classic setting of symmetric and independent private values. We show that the seller's optimal reserve price decreases in his own risk aversion, and more so in the first-price auction. The reserve price also decreases in the buyers' risk aversion in the first-price auction. Thus, greater risk aversion increases ex post efficiency in both auctions - especially that of the first-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 3 (May)
Pages: 1188-1202

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:3:p:1188-1202

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: First-price auction Second-price auction Risk aversion Reserve price;

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References

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  1. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  2. Smith, James L. & Levin, Dan, 1996. "Ranking Auctions with Risk Averse Bidders," Journal of Economic Theory, Elsevier, vol. 68(2), pages 549-561, February.
  3. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  4. Cox, James C & Smith, Vernon L & Walker, James M, 1988. " Theory and Individual Behavior of First-Price Auctions," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 61-99, March.
  5. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
  6. Esö, Péter & White, Lucy, 2003. "Precautionary Bidding in Auctions," CEPR Discussion Papers 3975, C.E.P.R. Discussion Papers.
  7. Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
  8. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-46, May.
  9. 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.
  10. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-92, June.
  11. Cox, James C. & Smith, Vernon L. & Walker, James M., 1982. "Auction market theory of heterogeneous bidders," Economics Letters, Elsevier, vol. 9(4), pages 319-325.
  12. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  13. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-99, November.
  14. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  15. Keith Waehrer & Ronald M. Harstad & Michael H. Rothkopf, 1998. "Auction Form Preferences of Risk-Averse Bid Takers," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 179-192, Spring.
  16. Holt, Charles A, Jr, 1980. "Competitive Bidding for Contracts under Alternative Auction Procedures," Journal of Political Economy, University of Chicago Press, vol. 88(3), pages 433-45, June.
  17. Levin, Dan & Smith, James L, 1994. "Equilibrium in Auctions with Entry," American Economic Review, American Economic Association, vol. 84(3), pages 585-99, June.
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Citations

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Cited by:
  1. Bettina Klose & Paul Schweinzer, 2012. "Auctioning risk: The all-pay auction under mean-variance preferences," ECON - Working Papers 097, Department of Economics - University of Zurich, revised Jun 2014.
  2. Brunner, Christoph & Hu, Audrey & Oechssler, Jörg, 2013. "Premium Auctions and Risk Preferences: An Experimental Study," Working Papers 0544, University of Heidelberg, Department of Economics.
  3. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
  4. Hu, Audrey, 2011. "How bidder's number affects optimal reserve price in first-price auctions under risk aversion," Economics Letters, Elsevier, vol. 113(1), pages 29-31, October.
  5. Bettina Klose & Paul Schweinzer, 2012. "Auctioning risk: The all-pay auction under mean-variance preferences," Discussion Papers 12/32, Department of Economics, University of York.
  6. Simon Loertscher & Andras Niedermayer, 2012. "Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation," Department of Economics - Working Papers Series 1162, The University of Melbourne.

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