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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.

Suggested Citation

  • Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1617-1635
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    References listed on IDEAS

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    1. Patrick Bajari, 2001. "Comparing competition and collusion: a numerical approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 187-205.
    2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, May.
    3. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    4. 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.
    5. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    6. Wayne-Roy Gayle & Jean Richard, 2008. "Numerical Solutions of Asymmetric, First-Price, Independent Private Values Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 32(3), pages 245-278, October.
    7. Cantillon, Estelle, 2008. "The effect of bidders' asymmetries on expected revenue in auctions," Games and Economic Behavior, Elsevier, vol. 62(1), pages 1-25, January.
    8. 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.
    9. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    10. Ed Hopkins, 2007. "Rank-Based Methods for the Analysis of Auctions," ESE Discussion Papers 173, Edinburgh School of Economics, University of Edinburgh.
    11. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    12. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    13. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    14. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    15. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
    16. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
    17. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    18. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 393-418.
    19. Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2002. "Low and high types in asymmetric first-price auctions," Economics Letters, Elsevier, vol. 75(2), pages 283-287, April.
    20. Blume, Andreas & Heidhues, Paul, 2004. "All equilibria of the Vickrey auction," Journal of Economic Theory, Elsevier, vol. 114(1), pages 170-177, January.
    21. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
    22. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    23. 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. 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.
    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. Fibich, Gadi & Gavish, Nir, 2011. "Numerical simulations of asymmetric first-price auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 479-495.
    4. 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.
    5. Kirkegaard, René & Overgaard, Per Baltzer, 2008. "Pre-auction offers in asymmetric first-price and second-price auctions," Games and Economic Behavior, Elsevier, vol. 63(1), pages 145-165, May.
    6. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    7. Lagerlöf, Johan N. M., 2012. "Does Cost Uncertainty in the Bertrand Model Soften Competition?," CEPR Discussion Papers 8817, C.E.P.R. Discussion Papers.
    8. repec:eee:matsoc:v:91:y:2018:i:c:p:51-55 is not listed on IDEAS
    9. Doni Nicola & Menicucci Domenico, 2013. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-33, September.
    10. Kirkegaard, René, 2014. "Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch," Games and Economic Behavior, Elsevier, vol. 85(C), pages 60-69.
    11. De Chiara, Alessandro, 2015. "Holding an Auction for the Wrong Project," MPRA Paper 72108, University Library of Munich, Germany, revised 21 Apr 2015.
    12. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
    13. 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.
    14. 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, Springer;Society for Computational Economics, vol. 42(2), pages 241-266, August.
    15. Timothy P. Hubbard & Rene Kirkegaard, 2015. "Asymmetric Auctions with More Than Two Bidders," Working Papers 1502, University of Guelph, Department of Economics and Finance.
    16. 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.
    17. repec:the:publsh:1824 is not listed on IDEAS
    18. repec:eee:jetheo:v:174:y:2018:i:c:p:1-15 is not listed on IDEAS

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