IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v19y2019i2p7n12.html
   My bibliography  Save this article

A First Price Auction with an Arbitrary Number of Asymmetric Bidders

Author

Listed:
  • Doni Nicola

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Via delle Pandette 32, I-50127Firenze (FI), Italy)

  • Menicucci Domenico

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Via delle Pandette 32, I-50127Firenze (FI), Italy)

Abstract

We examine an auction setting with private values and n≥2$n\geq 2$ bidders, which differ in the probability to have a low (high) value. We prove that for the first price auction, the equilibrium strategies can be written in closed form and there are gaps in the equilibrium bid distribution of each bidder except the strongest two. Our equilibrium characterization allows to prove that in this setting the seller prefers the second price auction to the first price auction for each n≥2$n\geq 2$.

Suggested Citation

  • Doni Nicola & Menicucci Domenico, 2019. "A First Price Auction with an Arbitrary Number of Asymmetric Bidders," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-7, June.
    • Handle: RePEc:bpj:bejtec:v:19:y:2019:i:2:p:7:n:12
    DOI: 10.1515/bejte-2018-0105
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/bejte-2018-0105
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/bejte-2018-0105?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
    3. 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.
    4. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
    5. 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.
    6. Maskin, Eric S & Riley, Joan G, 1985. "Auction Theory with Private Values," American Economic Review, American Economic Association, vol. 75(2), pages 150-155, May.
    7. Riley, John G, 1989. "Expected Revenue from Open and Sealed Bid Auctions," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 41-50, Summer.
    8. René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, vol. 80(5), pages 2349-2364, September.
    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. Kyungmin Kim & Youngwoo Koh, 2019. "Efficiency and Revenue in Asymmetric Auctions," Korean Economic Review, Korean Economic Association, vol. 35, pages 371-391.
    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. Kirkegaard, René, 2021. "Ranking reversals in asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    4. 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.
    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. 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. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 369-393, May.
    8. Bernard Lebrun, 2015. "Revenue-superior variants of the second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 245-275, June.
    9. Bobkova, Nina, 2020. "Asymmetric budget constraints in a first-price auction," Journal of Economic Theory, Elsevier, vol. 186(C).
    10. Sanyyam Khurana, 2020. "Asymmetric auctions with risk averse preferences," Working papers 304, Centre for Development Economics, Delhi School of Economics.
    11. Timothy C. Au & David Banks & Yi Guo, 2021. "Numerical Solution of Asymmetric Auctions," Decision Analysis, INFORMS, vol. 18(4), pages 321-334, December.
    12. Ethem Akyol, 2022. "Ex-Ante Welfare Superiority of the Boston Mechanism Over the Deferred Acceptance Mechanism," Dynamic Games and Applications, Springer, vol. 12(4), pages 1189-1220, December.
    13. 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.
    14. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    15. Werner Güth & Radosveta Ivanova–Stenzel & Manfred Königstein & Martin Strobel, 2002. "Bid Functions in Auctions and Fair Division Games: Experimental Evidence," German Economic Review, Verein für Socialpolitik, vol. 3(4), pages 461-484, November.
    16. Yuen Leng Chow & Joseph T.L. Ooi, 2014. "First-Price Sealed-Bid Tender versus English Open Auction: Evidence from Land Auctions," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 42(2), pages 253-278, June.
    17. Rosa, Benjamin V., 2020. "Affirmative action subcontracting regulations in dynamic procurement auctions," International Journal of Industrial Organization, Elsevier, vol. 72(C).
    18. Waterson, Michaël & Canoy, Marcel, 1994. "Tendering, auctions and preparation costs," CEPREMAP Working Papers (Couverture Orange) 9410, CEPREMAP.
    19. Hanming Fang & Stephen Morris, 2012. "Multidimensional Private Value Auctions," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 9, pages 319-356, World Scientific Publishing Co. Pte. Ltd..
    20. Bettina Klose & Paul Schweinzer, 2022. "Auctioning risk: the all-pay auction under mean-variance preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 881-916, June.

    More about this item

    Keywords

    first price auction; asymmetric bidders;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:bpj:bejtec:v:19:y:2019:i:2:p:7:n:12. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.