IDEAS home Printed from https://ideas.repec.org/p/cbt/econwp/10-17.html
   My bibliography  Save this paper

A Note on Log Concave Survivor Functions in Auctions

Author

Abstract

In a standard English auction in which bidders’ valuations are independently drawn from a common distribution, a standard regularity condition is that the survivor function of the distribution be log concave. In an auction where the seller sets a fixed price, the equivalent condition requires log concavity of a survivor function derived from the primitive distribution. In this note we show that log concavity of the primitive survivor function implies log concavity in the derived functions. This result is of interest when studying on-line auctions that combined aspects of fixed-price and English auctions.

Suggested Citation

  • Seamus Hogan & Laura Meriluoto, 2010. "A Note on Log Concave Survivor Functions in Auctions," Working Papers in Economics 10/17, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:10/17
    as

    Download full text from publisher

    File URL: https://repec.canterbury.ac.nz/cbt/econwp/1017.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Johannes Hörner & Larry Samuelson, 2011. "Managing Strategic Buyers," Journal of Political Economy, University of Chicago Press, vol. 119(3), pages 379-425.
    3. Kotowski, Maciej H., 2018. "On asymmetric reserve prices," Theoretical Economics, Econometric Society, vol. 13(1), January.
    4. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    5. Arozamena, Leandro & Weinschelbaum, Federico, 2009. "The effect of corruption on bidding behavior in first-price auctions," European Economic Review, Elsevier, vol. 53(6), pages 645-657, August.
    6. Milo Bianchi, 2013. "Immigration Policy and Self-Selecting Migrants," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(1), pages 1-23, February.
    7. Sheriff, Glenn, 2009. "Implementing second-best environmental policy under adverse selection," Journal of Environmental Economics and Management, Elsevier, vol. 57(3), pages 253-268, May.
    8. repec:dau:papers:123456789/5377 is not listed on IDEAS
    9. Takahashi, Hidenori, 2015. "Strategic design under uncertain evaluations : structural analysis of design-build auctions," Working Papers 15-08, University of Mannheim, Department of Economics.
    10. 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.
    11. Hernando-Veciana, Ángel & Tröge, Michael, 2011. "The insider's curse," Games and Economic Behavior, Elsevier, vol. 71(2), pages 339-350, March.
    12. Wasser, Cédric, 2013. "Bilateral k+1-price auctions with asymmetric shares and values," Games and Economic Behavior, Elsevier, vol. 82(C), pages 350-368.
    13. Bertoletti, Paolo, 2008. "A note on the Exclusion Principle," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1215-1218, December.
    14. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    15. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    16. 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.
    17. Mares, Vlad & Swinkels, Jeroen M., 2014. "On the analysis of asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 1-40.
    18. Ed Hopkins, 2007. "Rank-Based Methods for the Analysis of Auctions," Edinburgh School of Economics Discussion Paper Series 173, Edinburgh School of Economics, University of Edinburgh.
    19. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    20. 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.
    21. Ville Korpela, 2017. "All Deceptions Are Not Alike: Bayesian Mechanism Design with a Social Norm against Lying," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(2), pages 376-393, June.

    More about this item

    Keywords

    English Auction; Log Concavity; Survivor Function;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cbt:econwp:10/17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Albert Yee (email available below). General contact details of provider: https://edirc.repec.org/data/decannz.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.