IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v13y2013i1p33n9.html
   My bibliography  Save this article

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

Author

Listed:
  • Doni Nicola

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Firenze, Italy)

  • Menicucci Domenico

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Firenze, Italy)

Abstract

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. First, we characterize the unique equilibrium outcome in the first price auction for any values of parameters. Then we compare the first price auction with the second price auction in terms of expected revenue. Under the assumption that the probabilities of low values are the same for the two bidders, we obtain two main results: (i) the second price auction yields a higher revenue unless the distribution of a bidder’s valuation first-order stochastically dominates the distribution of the other bidder’s valuation “in a strong sense” and (ii) introducing reserve prices implies that the first price auction is never superior to the second price auction. In addition, in some cases, the revenue in the first price auction decreases when all the valuations increase.

Suggested Citation

  • 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 429-461, September.
    • Handle: RePEc:bpj:bejtec:v:13:y:2013:i:1:p:33:n:9
    DOI: 10.1515/bejte-2012-0014
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/bejte-2012-0014
    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-2012-0014?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    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 429-461, September.
    2. Nicola Doni & Domenico Menicucci, 2014. "Information Revelation in Procurement Auctions with Two‐Sided Asymmetric Information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(4), pages 952-968, December.
    3. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 439-454.
    4. 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.
    5. 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.
    6. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 369-393, May.
    7. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    8. 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.
    9. Rene Kirkegaard, 2011. "Ranking Asymmetric Auctions using the Dispersive Order," Working Papers 1101, University of Guelph, Department of Economics and Finance.
    10. Bernard Lebrun, 2002. "Continuity of the first price auction Nash equilibrium correspondence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 435-453.
    11. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
    12. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
    13. 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.
    14. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yew-Kwang Ng, 2016. "Are Unrealistic Assumptions/Simplifications Acceptable? Some Methodological Issues in Economics," Pacific Economic Review, Wiley Blackwell, vol. 21(2), pages 180-201, May.
    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 429-461, September.
    3. 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.
    4. Cohensius Gal & Segev Ella, 2018. "Sequential Bidding in Asymmetric First Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-21, January.
    5. Nicola Doni & Domenico Menicucci, 2014. "Information Revelation in Procurement Auctions with Two‐Sided Asymmetric Information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(4), pages 952-968, December.
    6. Kyungmin Kim & Youngwoo Koh, 2019. "Efficiency and Revenue in Asymmetric Auctions," Korean Economic Review, Korean Economic Association, vol. 35, pages 371-391.
    7. Kirkegaard, René, 2021. "Ranking reversals in asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    8. 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.

    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. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 369-393, May.
    2. 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.
    3. Sanyyam Khurana, 2020. "Asymmetric auctions with risk averse preferences," Working papers 304, Centre for Development Economics, Delhi School of Economics.
    4. 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.
    5. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    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. 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..
    8. 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.
    9. Lagerlof, Johan, 2012. "Does Cost Uncertainty in the Bertrand Model Soften Competition?," CEPR Discussion Papers 8817, C.E.P.R. Discussion Papers.
    10. Kirkegaard, René, 2021. "Ranking reversals in asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    11. Chaturvedi, Aadhaar, 2015. "Procurement auctions with capacity constrained suppliers," European Journal of Operational Research, Elsevier, vol. 247(3), pages 987-995.
    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. 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.
    14. Bobkova, Nina, 2020. "Asymmetric budget constraints in a first-price auction," Journal of Economic Theory, Elsevier, vol. 186(C).
    15. Rene Kirkegaard, 2005. "A Simple Approach to Analyzing Asymmetric First Price Auctions," Working Papers 0504, Brock University, Department of Economics, revised Nov 2005.
    16. Guido Tatone, 2018. "La reputazione negli appalti pubblici: uno strumento socialmente desiderabile per risolvere il problema dello scadimento qualitativo," ECONOMIA PUBBLICA, FrancoAngeli Editore, vol. 2018(1), pages 59-85.
    17. Elbittar, Alexander, 2009. "Impact of valuation ranking information on bidding in first-price auctions: A laboratory study," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 75-85, January.
    18. Timothy C. Au & David Banks & Yi Guo, 2021. "Numerical Solution of Asymmetric Auctions," Decision Analysis, INFORMS, vol. 18(4), pages 321-334, December.
    19. A. Alexander Elbittar, 2005. "Impact of Valuation Ranking Information on Bidding in First-Price," Microeconomics 0508008, University Library of Munich, Germany.
    20. Hafalir, Isa & Krishna, Vijay, 2009. "Revenue and efficiency effects of resale in first-price auctions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 589-602, September.

    More about this item

    Keywords

    asymmetric auctions; first price auctions; second price auctions;
    All these keywords.

    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:13:y:2013:i:1:p:33:n:9. 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.