IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v225y2015i1p141-16010.1007-s10479-012-1297-9.html
   My bibliography  Save this article

A parametric family of two ranked objects auctions: equilibria and associated risk

Author

Listed:
  • Estrella Alonso
  • Joaquin Sanchez-Soriano
  • Juan Tejada

Abstract

This paper deals with simultaneous auctions of two commonly ranked objects following the model studied in Menezes and Monteiro (J. Real Estate Finance Econ., 17(3):219–232, 1998 ). For these problems we introduce a parametric family of auction mechanisms which includes the three classic auctions (discriminatory-price auction, uniform-price auction and Vickrey auction) and we call it the $\mathcal{DUV}$ family. We provide the unique Bayesian Nash equilibrium for each auction in $\mathcal{DUV}$ and prove a revenue equivalence theorem for the parametric family. Likewise, we study the value at risk of the auctioneer as a reasonable decision criterion to determine which auctions in $\mathcal{DUV}$ may be better taking into account the interests of the auctioneer. We show that there are auction mechanisms in $\mathcal{DUV}$ which are better than the classic auction mechanisms with respect to this criterion. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Estrella Alonso & Joaquin Sanchez-Soriano & Juan Tejada, 2015. "A parametric family of two ranked objects auctions: equilibria and associated risk," Annals of Operations Research, Springer, vol. 225(1), pages 141-160, February.
    • Handle: RePEc:spr:annopr:v:225:y:2015:i:1:p:141-160:10.1007/s10479-012-1297-9
    DOI: 10.1007/s10479-012-1297-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1297-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1297-9?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. Juan Feng, 2008. "—Optimal Mechanism for Selling a Set of Commonly Ranked Objects," Marketing Science, INFORMS, vol. 27(3), pages 501-512, 05-06.
    2. Menezes, Flavio M & Monteiro, Paulo Klinger, 1998. "Simultaneous Pooled Auctions," The Journal of Real Estate Finance and Economics, Springer, vol. 17(3), pages 219-232, November.
    3. Keith Waehrer & Ronald M. Harstad & Michael H. Rothkopf, 1998. "Auction Form Preferences of Risk-Averse Bid Takers," RAND Journal of Economics, The RAND Corporation, vol. 29(1), pages 179-192, Spring.
    4. John C. Harsanyi, 1968. "Games with Incomplete Information Played by "Bayesian" Players Part II. Bayesian Equilibrium Points," Management Science, INFORMS, vol. 14(5), pages 320-334, January.
    5. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    6. Maarten C. W. Janssen & Vladimir A. Karamychev & Emiel Maasland, 2010. "Simultaneous Pooled Auctions with Multiple Bids and Preference Lists," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 166(2), pages 286-298, June.
    7. Lim, Wei Shi & Tang, Christopher S., 2006. "An auction model arising from an Internet search service provider," European Journal of Operational Research, Elsevier, vol. 172(3), pages 956-970, August.
    8. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    9. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    10. Marc S. Robinson, 1985. "Collusion and the Choice of Auction," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 141-145, Spring.
    11. Estrella Alonso & Juan Tejada, 2010. "Equivalencia de Ingresos en un Duopolio Eléctrico," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 47(136), pages 191-215.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    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. Estrella Alonso & Joaquín Sánchez-Soriano & Juan Tejada, 2020. "Mixed Mechanisms for Auctioning Ranked Items," Mathematics, MDPI, vol. 8(12), pages 1-26, December.

    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. Estrella Alonso & Joaquín Sánchez-Soriano & Juan Tejada, 2020. "Mixed Mechanisms for Auctioning Ranked Items," Mathematics, MDPI, vol. 8(12), pages 1-26, December.
    2. Committee, Nobel Prize, 2020. "Improvements to auction theory and inventions of new auction formats," Nobel Prize in Economics documents 2020-2, Nobel Prize Committee.
    3. Garrett van Ryzin & Gustavo Vulcano, 2004. "Optimal Auctioning and Ordering in an Infinite Horizon Inventory-Pricing System," Operations Research, INFORMS, vol. 52(3), pages 346-367, June.
    4. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    5. Matthew J. Clayton & S. Abraham Ravid, 1999. "The Effect of Leverage on Bidding Behavior: Theory and Evidence from the FCC Auctions," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-055, New York University, Leonard N. Stern School of Business-.
    6. Hongjun Zhong, 2002. "postbid market interaction and auction choice," Microeconomics 0210002, University Library of Munich, Germany.
    7. Kang, Chao-Chung & Lee, Tsun-Siou & Huang, Szu-Chi, 2013. "Royalty bargaining in Public–Private Partnership projects: Insights from a theoretic three-stage game auction model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 59(C), pages 1-14.
    8. Page Jr., F.H., 1994. "Optimal Auction Design with Risk Aversion and Correlated Information," Other publications TiSEM ac23fdfa-b35c-4015-9c5c-e, Tilburg University, School of Economics and Management.
    9. Page Jr., Frank H., 1998. "Existence of optimal auctions in general environments," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 389-418, May.
    10. Marshall, Robert C. & Marx, Leslie M., 2007. "Bidder collusion," Journal of Economic Theory, Elsevier, vol. 133(1), pages 374-402, March.
    11. 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.
    12. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    13. Vasserman, Shoshana & Watt, Mitchell, 2021. "Risk aversion and auction design: Theoretical and empirical evidence," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    14. Roberto Burguet, 2000. "Auction theory: a guided tour," Investigaciones Economicas, Fundación SEPI, vol. 24(1), pages 3-50, January.
    15. Fibich, Gadi & Gavious, Arieh, 2010. "Asymptotic revenue equivalence of asymmetric auctions with interdependent values," European Journal of Operational Research, Elsevier, vol. 206(2), pages 496-507, October.
    16. Zhao, Guo, 2015. "Dynamic Games under Bounded Rationality," MPRA Paper 62688, University Library of Munich, Germany.
    17. Hu, Audrey & Matthews, Steven A. & Zou, Liang, 2010. "Risk aversion and optimal reserve prices in first- and second-price auctions," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1188-1202, May.
    18. Etro, Federico, 2017. "Research in economics and game theory. A 70th anniversary," Research in Economics, Elsevier, vol. 71(1), pages 1-7.
    19. Dutra, Renato Cabral Dias & Carpio, Lucio Guido Tapia, 2021. "Biodiesel auctions in Brazil: Symmetry of bids and informational paradigm," Renewable and Sustainable Energy Reviews, Elsevier, vol. 137(C).
    20. Page Jr., F.H., 1994. "Optimal Auction Design with Risk Aversion and Correlated Information," Discussion Paper 1994-109, Tilburg University, Center for Economic Research.

    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:spr:annopr:v:225:y:2015:i:1:p:141-160:10.1007/s10479-012-1297-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.