IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v251y2025ics0165176525001363.html

The three-player lowest unique number game

Author

Listed:
  • Sentes, Balázs

Abstract

This paper characterizes the unique symmetric mixed-strategy Nash equilibrium in the three-player version Lowest Unique Number Game. In this game, each player chooses a positive integer simultaneously and the player with the lowest unique number wins. The equilibrium mixing is shown to have full support and it is characterized by a constant hazard rate which is around .46.

Suggested Citation

  • Sentes, Balázs, 2025. "The three-player lowest unique number game," Economics Letters, Elsevier, vol. 251(C).
    • Handle: RePEc:eee:ecolet:v:251:y:2025:i:c:s0165176525001363
    DOI: 10.1016/j.econlet.2025.112299
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176525001363
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2025.112299?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Robert Östling & Joseph Tao-yi Wang & Eileen Y. Chou & Colin F. Camerer, 2011. "Testing Game Theory in the Field: Swedish LUPI Lottery Games," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 1-33, August.
    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. Pierre Bernhard & Marc Deschamps, 2017. "On Dynamic Games with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 7(3), pages 360-385, September.
    2. Eichberger, Jürgen & Vinogradov, Dmitri, 2016. "Efficiency of Lowest-Unmatched Price Auctions," Economics Letters, Elsevier, vol. 141(C), pages 98-102.
    3. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    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. Toomas Hinnosaar, 2013. "Penny Auctions are Unpredictable," Carlo Alberto Notebooks 305, Collegio Carlo Alberto.
    6. Yuxin Chen & Ozge Turut, 2018. "Entry deterrence/accommodation with imperfect strategic thinking capability," Quantitative Marketing and Economics (QME), Springer, vol. 16(2), pages 175-207, June.
    7. 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.
    8. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    9. Nir Halevy, 2020. "Strategic thinking and behavior during a pandemic," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 15(5), pages 648-659, September.
    10. Andrea Gallice, 2010. "Price Reveal Auctions on the Internet," Carlo Alberto Notebooks 147, Collegio Carlo Alberto.
    11. Andrea Gallice & Giuseppe Sorrenti, 2022. "Curious about the price? Consumers’ behavior in price reveal auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 29(9), pages 831-834, May.
    12. Yuhong Xu & Shih-Fen Cheng & Xinyu Chen, 2023. "Improving Quantal Cognitive Hierarchy Model Through Iterative Population Learning," Papers 2302.06033, arXiv.org, revised Feb 2023.
    13. Koriyama, Yukio & Ozkes, Ali I., 2021. "Inclusive cognitive hierarchy," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 458-480.
    14. 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.
    15. Tore Ellingsen & Robert Östling, 2010. "When Does Communication Improve Coordination?," American Economic Review, American Economic Association, vol. 100(4), pages 1695-1724, September.
    16. Hinnosaar, Toomas, 2016. "Penny auctions," International Journal of Industrial Organization, Elsevier, vol. 48(C), pages 59-87.
    17. Daniel Carvalho & Luís Santos-Pinto, 2014. "A cognitive hierarchy model of behavior in the action commitment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 551-577, August.
    18. David Gill & Victoria Prowse, 2016. "Cognitive Ability, Character Skills, and Learning to Play Equilibrium: A Level-k Analysis," Journal of Political Economy, University of Chicago Press, vol. 124(6), pages 1619-1676.
    19. 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.
    20. Damian S. Damianov & Ronald Peeters, 2018. "Prize‐Based Mechanisms For Fund‐Raising: Theory And Experiments," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1562-1584, July.

    More about this item

    Keywords

    ;

    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:eee:ecolet:v:251:y:2025:i:c:s0165176525001363. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.