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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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  • 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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    2. 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.
    3. Baisa, Brian & Burkett, Justin, 2018. "Large multi-unit auctions with a large bidder," Journal of Economic Theory, Elsevier, vol. 174(C), pages 1-15.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Lagerlöf, Johan N. M., 2012. "Does Cost Uncertainty in the Bertrand Model Soften Competition?," CEPR Discussion Papers 8817, C.E.P.R. Discussion Papers.
    9. Lorentziadis, Panos L., 2020. "Competitive bidding in asymmetric multidimensional public procurement," European Journal of Operational Research, Elsevier, vol. 282(1), pages 211-220.
    10. Tristan Gagnon-Bartsch & Marco Pagnozzi & Antonio Rosato, 2020. "Projection of Private Values in Auctions," CSEF Working Papers 571, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    11. 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.
    12. 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.
    13. Timothy P. Hubbard & Rene Kirkegaard, 2015. "Asymmetric Auctions with More Than Two Bidders," Working Papers 1502, University of Guelph, Department of Economics and Finance.
    14. 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.
    15. Kotowski, Maciej H., 2018. "On asymmetric reserve prices," Theoretical Economics, Econometric Society, vol. 13(1), January.
    16. 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.
    17. Burkett, Justin & Woodward, Kyle, 2020. "Uniform price auctions with a last accepted bid pricing rule," Journal of Economic Theory, Elsevier, vol. 185(C).
    18. De Chiara, Alessandro, 2015. "Holding an Auction for the Wrong Project," MPRA Paper 72108, University Library of Munich, Germany, revised 21 Apr 2015.
    19. 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.
    20. Sanyyam Khurana, 2020. "Asymmetric auctions with risk averse preferences," Working papers 304, Centre for Development Economics, Delhi School of Economics.
    21. Sanyyam Khurana, 2020. "Unraveling of Value-Rankings in Auctions with Resale," Working papers 308, Centre for Development Economics, Delhi School of Economics.
    22. Minchuk, Yizhaq & Sela, Aner, 2018. "Prebidding first-price auctions with and without head starts," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 51-55.
    23. 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.

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