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Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions

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Author Info
Ed Hopkins (University of Edinburgh)
Tatiana Kornienko (University of Stirling)

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Abstract

This paper analyses comparative statics for first price auctions and all pay auctions with independent private values. In all pay auctions, bidders with low values will respond to a stochastically higher (in the sense of likelihood ratio dominance) distribution of types by playing less aggressively while high value bidders bid more. In the first price auction, a similar change results in all types playing more aggressively. Furthermore, we show that a decrease in dispersion of values, in the sense of a refinement of second order stochastic dominance, although also associated with an increase in competitiveness, may in addition result in less aggressive play by bidders with high values in both auction forms. We also find similar considerations in an oligopoly game with incomplete information: stochastically lower costs can lead to higher prices.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Topics in Theoretical Economics.

Volume (Year): 7 (2007)
Issue (Month): 1 ()
Pages: 1366-1366
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Handle: RePEc:bep:thetop:v:7:y:2007:i:1:p:1366-1366

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Related research
Keywords: auctions likelihood ratio comparative statics games of incomplete information

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September. [Downloadable!] (restricted)
  2. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2005. "The Theory of Assortative Matching Based on Costly Signals," Discussion Papers 85, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
    Other versions:
  3. Ed Hopkins & Tatiana Kornienko, 2004. "Running to Keep in the Same Place: Consumer Choice as a Game of Status," ESE Discussion Papers 92, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  4. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February. [Downloadable!] (restricted)
    Other versions:
  5. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. Jacob K. Goeree & Theo Offerman, 2003. "Competitive Bidding in Auctions with Private and Common Values," Economic Journal, Royal Economic Society, vol. 113(489), pages 598-613, 07. [Downloadable!] (restricted)
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  8. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October. [Downloadable!] (restricted)
  9. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February. [Downloadable!] (restricted)
  10. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June. [Downloadable!] (restricted)
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  11. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn. [Downloadable!] (restricted)
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  12. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September. [Downloadable!] (restricted)
  13. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 439-54, July.
  14. Kyle Bagwell & Asher Wolinsky, 2002. "Game theory and industrial organization," Discussion Papers 0102-36, Columbia University, Department of Economics. [Downloadable!]
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  15. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June. [Downloadable!] (restricted)
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  16. Ramos, Hector M. & Ollero, Jorge & Sordo, Miguel A., 2000. "A Sufficient Condition for Generalized Lorenz Order," Journal of Economic Theory, Elsevier, vol. 90(2), pages 286-292, February. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ed Hopkins, 2008. "Rank-Based Methods for the Analysis of Auctions," Levine's Bibliography 122247000000001900, UCLA Department of Economics. [Downloadable!]
  2. Ed Hopkins, 2007. "Rank-Based Methods for the Analysis of Auctions," ESE Discussion Papers 173, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  3. René Kirkegaard, 2007. "Comparative Statics and Welfare in Heterogeneous Contests: Bribes, Caps, and Performance Thresholds," Working Papers 0702, Brock University, Department of Economics. [Downloadable!]
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