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Risk Aversion and Optimal Reserve Prices in First and Second-Price Auctions

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Author Info

  • Audrey Hu

    ()
    (Tinbergen Institute, University of Amsterdam)

  • Steven A. Matthews

    ()
    (Department of Economics, University of Pennsylvania)

  • Liang Zou

    ()
    (Faculty of Economics and Business, University of Amsterdam)

Abstract

This paper analyzes the effects of buyer and seller risk aversion in first and second-price auctions. The setting is the classic one of symmetric and independent private values, with ex ante homogeneous bidders. However, the seller is able to optimally set the reserve price. In both auctions the seller’s optimal reserve price is shown to decrease in his own risk aversion, and more so in the first-price auction. Thus, greater seller risk aversion increases the ex post efficiency of both auctions, and especially that of the first-price auction. The seller’s optimal reserve price in the first-price, but not in the second-price, auction decreases in the buyers’ risk aversion. Thus, greater buyer risk aversion also increases the ex post efficiency of the first but not the second-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

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-016.

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Length: 22 pages
Date of creation: 22 Apr 2009
Date of revision:
Handle: RePEc:pen:papers:09-016

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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. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
  2. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  5. 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.
  6. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  7. 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.
  8. Eric Maskin & John Riley, 2003. "Uniqueness of Equilibrium in Sealed High-Bid Auctions," Economics Working Papers 0031, Institute for Advanced Study, School of Social Science.
  9. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
  10. 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.
  11. Péter Esö & Lucy White, 2004. "Precautionary Bidding in Auctions," Econometrica, Econometric Society, vol. 72(1), pages 77-92, 01.
  12. Smith, James L. & Levin, Dan, 1996. "Ranking Auctions with Risk Averse Bidders," Journal of Economic Theory, Elsevier, vol. 68(2), pages 549-561, February.
  13. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  14. Harris, Milton & Raviv, Artur, 1981. "Allocation Mechanisms and the Design of Auctions," Econometrica, Econometric Society, vol. 49(6), pages 1477-99, November.
  15. Levin, Dan & Smith, James L, 1994. "Equilibrium in Auctions with Entry," American Economic Review, American Economic Association, vol. 84(3), pages 585-99, June.
  16. 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.
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Cited by:
  1. Brunner, Christoph & Hu, Audrey & Oechssler, Jörg, 2013. "Premium Auctions and Risk Preferences: An Experimental Study," Working Papers 0544, University of Heidelberg, Department of Economics.
  2. Loertscher, Simon & Niedermayer, Andras, 2012. "Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 434, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  3. 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.
  4. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
  5. 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.
  6. 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.

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