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Auctioning risk: The all-pay auction under mean-variance preferences

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  • Bettina Klose
  • Paul Schweinzer
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    Abstract

    We develop the idea of using mean-variance preferences for the analysis of the first-price, all-pay auction. On the bidding side, we characterise the optimal strategy in symmetric allpay auctions under mean-variance preferences for general distributions of valuations and any number of bidders. We find that, in contrast to winner-pay auction formats, only hightype bidders increase their bids relative to the risk-neutral case while low types minimise variance exposure by bidding low. Introducing asymmetric variance aversions across bidders into a Uniform valuations, two-player framework, we show that a more variance-averse type bids always higher than her less variance-averse counterpart. Taking mean-variance bidding behaviour as given, we show that an expected revenue maximising seller may want to optimally limit the number of participants. Although expected revenue for risk-neutral bidders typically dominates revenue under mean-variance bidding, if the seller himself takes account of the variance of revenue, he may find it preferable to attract bidders endowed with mean-variance preferences.

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    Bibliographic Info

    Paper provided by Department of Economics, University of York in its series Discussion Papers with number 12/32.

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    Date of creation: Nov 2012
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    Handle: RePEc:yor:yorken:12/32

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    Keywords: Auctions; Contests; Mean-Variance preferences;

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    1. Eso, Peter & Futo, Gabor, 1999. "Auction design with a risk averse seller," Economics Letters, Elsevier, vol. 65(1), pages 71-74, October.
    2. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Hu, Audrey & Matthews, Steven A. & Zou, Liang, 2010. "Risk aversion and optimal reserve prices in first- and second-price auctions," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1188-1202, May.
    4. Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
    5. Audrey Hu & Steven A. Matthews & Liang Zou, 2009. "Risk Aversion and Optimal Reserve Prices in First and Second-Price Auctions, Second Version," PIER Working Paper Archive 10-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Jan 2010.
    6. Esö, Péter & White, Lucy, 2003. "Precautionary Bidding in Auctions," CEPR Discussion Papers 3975, C.E.P.R. Discussion Papers.
    7. René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, Econometric Society, vol. 80(5), pages 2349-2364, 09.
    8. Holt, Charles A, Jr, 1980. "Competitive Bidding for Contracts under Alternative Auction Procedures," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 88(3), pages 433-45, June.
    9. Subir Bose & Arup Daripa, 2008. "A Dynamic Mechanism and Surplus Extraction Under Ambiguity," Discussion Papers in Economics 08/24, Department of Economics, University of Leicester.
    10. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer, vol. 50(2), pages 269-302, June.
    11. Steven A. Matthews, 1985. "Comparing Auctions for Risk Averse Buyers: A Buyer's Pointof View," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 664R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Saha, Atanu, 1997. "Risk Preference Estimation in the Nonlinear Mean Standard Deviation Approach," Economic Inquiry, Western Economic Association International, Western Economic Association International, vol. 35(4), pages 770-82, October.
    13. Alex Robson, 2012. "Contests between players with mean-variance preferences," Discussion Papers in Economics economics:201207, Griffith University, Department of Accounting, Finance and Economics.
    14. Smith, James L. & Levin, Dan, 1996. "Ranking Auctions with Risk Averse Bidders," Journal of Economic Theory, Elsevier, vol. 68(2), pages 549-561, February.
    15. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
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