IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v50y2021i1d10.1007_s00182-020-00740-2.html
   My bibliography  Save this article

Option values in sequential auctions with time-varying valuations

Author

Listed:
  • Amir Ban

    (Weizmann Institute of Science)

  • Ron Lavi

    (Technion, Israel Institute of Technology)

Abstract

We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are not necessarily efficient, but we show that when bidder valuations satisfy a certain constraint, an efficient equilibrium always exists. This result may be extended to a model with arrivals of bidders. We show how the equilibrium allocation, bids, and bidder utilities are calculated in the general case. We prove constructively that a pure subgame-perfect equilibrium always exists, and show how all pure equilibria can be found by the method of option values

Suggested Citation

  • Amir Ban & Ron Lavi, 2021. "Option values in sequential auctions with time-varying valuations," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 75-104, March.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:1:d:10.1007_s00182-020-00740-2
    DOI: 10.1007/s00182-020-00740-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-020-00740-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-020-00740-2?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. Gale, Ian L. & Stegeman, Mark, 2001. "Sequential Auctions of Endogenously Valued Objects," Games and Economic Behavior, Elsevier, vol. 36(1), pages 74-103, July.
    2. Bernhardt, Dan & Scoones, David, 1994. "A Note on Sequential Auctions," American Economic Review, American Economic Association, vol. 84(3), pages 653-657, June.
    3. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(1), pages 1-31.
    4. Hal R. Varian & Christopher Harris, 2014. "The VCG Auction in Theory and Practice," American Economic Review, American Economic Association, vol. 104(5), pages 442-445, May.
    5. Kala Krishna, 1999. "Auctions with endogenous valuations: the snowball effect revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 377-391.
    6. Engelbrecht-Wiggans, Richard, 1994. "Sequential auctions of stochastically equivalent objects," Economics Letters, Elsevier, vol. 44(1-2), pages 87-90.
    7. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    8. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    9. Vishnu V. Narayan & Enguerrand Prebet & Adrian Vetta, 2019. "The Declining Price Anomaly is not Universal in Multi-Buyer Sequential Auctions (but almost is)," Papers 1905.00853, arXiv.org.
    10. Said, Maher, 2011. "Sequential auctions with randomly arriving buyers," Games and Economic Behavior, Elsevier, vol. 73(1), pages 236-243, September.
    11. Marc Dudey, 1992. "Dynamic Edgeworth-Bertrand Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1461-1477.
    12. Krishna, Kala, 1993. "Auctions with Endogenous Valuations: The Persistence of Monopoly Revisited," American Economic Review, American Economic Association, vol. 83(1), pages 147-160, March.
    13. Caragiannis, Ioannis & Kaklamanis, Christos & Kanellopoulos, Panagiotis & Kyropoulou, Maria & Lucier, Brendan & Paes Leme, Renato & Tardos, Éva, 2015. "Bounding the inefficiency of outcomes in generalized second price auctions," Journal of Economic Theory, Elsevier, vol. 156(C), pages 343-388.
    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. Bruno Larue & Mohamed Jeddy & Sébastien Pouliot, 2013. "On the Number of Bidders and Auction Performance: when More Means Less," Cahiers de recherche CREATE 2013-4, CREATE.
    2. Bruno Larue & Sébastien Pouliot & Mohamed Jeddy, 2016. "On the Number and Heterogeneity of Bidders in Livestock Auctions," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 64(2), pages 289-310, June.
    3. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    4. Jeddy, Mohamed & Larue, Bruno, 2012. "Mergers, concurrent marketing mechanisms and the performance of sequential auctions," Working Papers 126945, Structure and Performance of Agriculture and Agri-products Industry (SPAA).
    5. Gale, Ian L. & Stegeman, Mark, 2001. "Sequential Auctions of Endogenously Valued Objects," Games and Economic Behavior, Elsevier, vol. 36(1), pages 74-103, July.
    6. Dütting, Paul & Fischer, Felix & Parkes, David C., 2019. "Expressiveness and robustness of first-price position auctions," LSE Research Online Documents on Economics 85877, London School of Economics and Political Science, LSE Library.
    7. Mezzetti, Claudio, 2008. "Aversion to Price Risk and the Afternoon Effect," The Warwick Economics Research Paper Series (TWERPS) 857, University of Warwick, Department of Economics.
    8. Patrick Hummel, 2018. "Hybrid mechanisms for Vickrey–Clarke–Groves and generalized second-price bids," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 331-350, March.
    9. Rosato, Antonio, 2014. "Loss Aversion in Sequential Auctions: Endogenous Interdependence, Informational Externalities and the "Afternoon Effect"," MPRA Paper 56824, University Library of Munich, Germany.
    10. repec:ebl:ecbull:v:30:y:2010:i:1:p:429-436 is not listed on IDEAS
    11. Dennis Clerck & Erik Demeulemeester, 2016. "A sequential procurement model for a PPP project pipeline," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 427-457, March.
    12. Donna, Javier & Espin-Sanchez, Jose, 2014. "Complements and Substitutes in Sequential Auctions: The Case of Water Auctions," MPRA Paper 55079, University Library of Munich, Germany.
    13. Eric Overby & Karthik Kannan, 2015. "How Reduced Search Costs and the Distribution of Bidder Participation Affect Auction Prices," Management Science, INFORMS, vol. 61(6), pages 1398-1420, June.
    14. Paul Dütting & Felix Fischer & David C. Parkes, 2019. "Expressiveness and Robustness of First-Price Position Auctions," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 196-211, February.
    15. Alison Watts, 2018. "Generalized Second Price Auctions over a Network," Games, MDPI, vol. 9(3), pages 1-11, September.
    16. Frank Kelly & Peter Key & Neil Walton, 2016. "Efficient Advert Assignment," Operations Research, INFORMS, vol. 64(4), pages 822-837, August.
    17. Giorgio Bellettini & Gianmarco I. P. Ottaviano, 2005. "Special Interests and Technological Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 43-56.
    18. Bergemann, Dirk & Valimaki, Juuso, 2003. "Dynamic common agency," Journal of Economic Theory, Elsevier, vol. 111(1), pages 23-48, July.
    19. José Alcalde & Matthias Dahm, "undated". "Supplier Diversity before the Time of Cholera," Discussion Papers in Economics 20/07, Division of Economics, School of Business, University of Leicester.
    20. Axel Ockenfels & David Reiley & Abdolkarim Sadrieh, 2006. "Online Auctions," NBER Working Papers 12785, National Bureau of Economic Research, Inc.
    21. Emmanuel LORENZON, 2020. "Uninformed Bidding in Sequential Auctions," Bordeaux Economics Working Papers 2020-20, Bordeaux School of Economics (BSE).

    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:jogath:v:50:y:2021:i:1:d:10.1007_s00182-020-00740-2. 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.