IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00681002.html
   My bibliography  Save this paper

Equilibrium strategy and population-size effects in lowest unique bid auctions

Author

Listed:
  • Simone Pigolotti

    (NBI - Niels Bohr Institute [Copenhagen] - Faculty of Science [Copenhagen] - UCPH - University of Copenhagen = Københavns Universitet, Dept. de Fisica i Eng. Nuclear - UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona])

  • Sebastian Bernhardsson

    (NBI - Niels Bohr Institute [Copenhagen] - Faculty of Science [Copenhagen] - UCPH - University of Copenhagen = Københavns Universitet, FOI - Swedish Defence Research Agency [Stockholm])

  • Jeppe Juul

    (NBI - Niels Bohr Institute [Copenhagen] - Faculty of Science [Copenhagen] - UCPH - University of Copenhagen = Københavns Universitet)

  • Gorm Galster

    (NBI - Niels Bohr Institute [Copenhagen] - Faculty of Science [Copenhagen] - UCPH - University of Copenhagen = Københavns Universitet)

  • Pierpaolo Vivo

    (LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique)

Abstract

In lowest unique bid auctions, $N$ players bid for an item. The winner is whoever places the \emph{lowest} bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large dataset of internet auctions. The theory agrees with the data with striking accuracy for small population size $N$, while for larger $N$ a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.

Suggested Citation

  • Simone Pigolotti & Sebastian Bernhardsson & Jeppe Juul & Gorm Galster & Pierpaolo Vivo, 2012. "Equilibrium strategy and population-size effects in lowest unique bid auctions," Post-Print hal-00681002, HAL.
    • Handle: RePEc:hal:journl:hal-00681002
    DOI: 10.1103/PhysRevLett.108.088701
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Yamada, Takashi & Hanaki, Nobuyuki, 2016. "An experiment on Lowest Unique Integer Games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 88-102.
    2. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    3. Cancan Zhou & Hongguang Dong & Rui Hu & Qinghua Chen, 2015. "Smarter than Others? Conjectures in Lowest Unique Bid Auctions," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-13, April.
    4. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2015. "Lowest unique bid auctions with population uncertainty," Economics Letters, Elsevier, vol. 134(C), pages 53-57.
    5. Berger, Ulrich & De Silva, Hannelore & Fellner-Röhling, Gerlinde, 2016. "Cognitive hierarchies in the minimizer game," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 337-348.
    6. Rui Hu & Jinzhong Guo & Qinghua Chen & Tao Zheng, 2017. "The Psychological Force Model for Lowest Unique Bid Auction," Computational Economics, Springer;Society for Computational Economics, vol. 50(4), pages 655-667, December.
    7. Arvind Srinivasan & Burton Simon, 2024. "Exact asymptotics and continuous approximations for the Lowest Unique Positive Integer game," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 653-671, June.

    More about this item

    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:hal:journl:hal-00681002. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.