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Asymmetric first price auctions

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  • Kirkegaard, René

Abstract

A new approach to asymmetric first price auctions is proposed which circumvents the need to examine bidding strategies directly. Specifically, the ratio of bidders' (endogenous) payoffs is analyzed and compared to the ratio of the (exogenous) distribution functions that describe beliefs. Most of the results are inferred from this comparison. In the existing theoretical literature, assumptions of first order stochastic dominance or stronger imply that the latter ratio has very specific properties, but no such assumptions are imposed here. It is proven that first order stochastic dominance is necessary for bidding strategies not to cross. When this assumption is relaxed in the numerical literature it is done in a manner that leads to exactly one crossing. However, it is straightforward to construct examples with several crossings. Finally, bid distributions will cross in auctions with two bidders whenever second order (but not first order) stochastic dominance applies.

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Bibliographic Info

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

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1617-1635

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1617-1635

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

Related research

Keywords: Asymmetric auctions First price auctions;

References

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  1. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-92, June.
  2. 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.
  3. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
  4. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
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  8. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  9. Patrick Bajari, 2001. "Comparing competition and collusion: a numerical approach," Economic Theory, Springer, vol. 18(1), pages 187-205.
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  13. 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.
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  17. Hopkins Ed & Kornienko Tatiana, 2007. "Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-25, May.
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Citations

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Cited by:
  1. Hikmet Gunay & Xin Meng & Mark Nagelberg, 2012. "Reserve Price When Bidders are Asymmetric," ISER Discussion Paper 0849, Institute of Social and Economic Research, Osaka University.
  2. Timothy P. Hubbard & Harry J. Paarsch, 2012. "On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm," Carlo Alberto Notebooks 291, Collegio Carlo Alberto.
  3. Kirkegaard, René & Per Baltzer Overgaard, 2005. "Pre-Auction Offers in Asymmetric First-Price and Second-Price Auctions," Economics Working Papers 2005-17, School of Economics and Management, University of Aarhus.
  4. Nicola Doni & Domenico Menicucci, 2011. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," Economics Working Papers ECO2011/27, European University Institute.
  5. Johan N.M. Lagerlöf, 2013. "Does Cost Uncertainty in the Bertrand Model Soften Competition?," Discussion Papers 14-08, University of Copenhagen. Department of Economics.
  6. Yizhaq Minchuk, 2013. "Low and High Types of Bidders in Asymmetric Auctions with A General Utility Function," Economics Bulletin, AccessEcon, vol. 33(2), pages 1328-1332.
  7. De Silva, Dakshina G. & Hubbard, Timothy P. & Kosmopoulou, Georgia, 2013. "Efficacy of a Bidder Training Program: Lessons from LINC," MPRA Paper 51329, University Library of Munich, Germany.
  8. Timothy Hubbard & René Kirkegaard & Harry Paarsch, 2013. "Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions," Computational Economics, Society for Computational Economics, vol. 42(2), pages 241-266, August.
  9. Lescourret, Laurence & Robert, Christian Y., 2011. "Transparency matters: Price formation in the presence of order preferencing," Journal of Financial Markets, Elsevier, vol. 14(2), pages 227-258, May.
  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.

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