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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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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.

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