IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2023-05.html
   My bibliography  Save this paper

Show your strength in the hammer-nail game: a Nim game with incomplete information

Author

Listed:
  • Gisèle Umbhauer

Abstract

We study the hammer-nail game, a game played in the French TV show “Fort Boyard”, by transforming this game into a Nim game with incomplete information. In this game, two players are in front of a nail slightly driven into a wooden support. Both have a hammer and in turn hit the nail. The winner is the first player able to fully drive the nail into the support. A player is of strength f if he is able, with one swing of the hammer, to drive the nail at most f millimeters into the support. We study the perfect Bayesian Nash equilibria of this game with incomplete information on the players’strength, and we also look at the equilibrium behavior when strength is combined with dexterity.

Suggested Citation

  • Gisèle Umbhauer, 2023. "Show your strength in the hammer-nail game: a Nim game with incomplete information," Working Papers of BETA 2023-05, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2023-05
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2023/2023-05.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gisele Umbhauer, 2016. "Game theory and exercices [Théorie des jeux et exercices]," Post-Print hal-01762122, HAL.
    2. Gneezy, Uri & Rustichini, Aldo & Vostroknutov, Alexander, 2010. "Experience and insight in the Race game," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 144-155, August.
    3. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    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. Gisèle Umbhauer, 2023. "A sad lesson from the hammer-nail game: strength is better than dexterity," Working Papers of BETA 2023-31, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.

    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. Charness, Gary & Le Bihan, Yves & Villeval, Marie Claire, 2024. "Mindfulness training, cognitive performance and stress reduction," Journal of Economic Behavior & Organization, Elsevier, vol. 217(C), pages 207-226.
    2. Nobuyuki Hanaki & Eizo Akiyama & Yukihiko Funaki & Ryuichiro Ishikawa, 2017. "Diversity in Cognitive Ability Enlarges Mispricing in Experimental Asset Markets," GREDEG Working Papers 2017-08, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    3. Chen, Daniel & Hopfensitz, Astrid & van Leeuwen, Boris & van de Ven, Jeroen, 2019. "The Strategic Display of Emotions," Other publications TiSEM ab45cbcc-1ea1-4762-b5c9-e, Tilburg University, School of Economics and Management.
    4. Nobuyuki Hanaki & Keigo Inukai & Takehito Masuda & Yuta Shimodaira, 2021. "Participants’ Characteristics at ISER-Lab in 2020," ISER Discussion Paper 1141, Institute of Social and Economic Research, Osaka University.
    5. Grandjean, Gilles & Lefebvre, Mathieu & Mantovani, Marco, 2022. "Preferences and strategic behavior in public goods games," Journal of Economic Behavior & Organization, Elsevier, vol. 195(C), pages 171-185.
    6. Bayer, R.-C. & Renou, Ludovic, 2016. "Logical abilities and behavior in strategic-form games," Journal of Economic Psychology, Elsevier, vol. 56(C), pages 39-59.
    7. Wei James Chen & Joseph Tao-yi Wang, 2020. "A modified Monty Hall problem," Theory and Decision, Springer, vol. 89(2), pages 151-156, September.
    8. Masiliūnas, Aidas, 2023. "Learning in rent-seeking contests with payoff risk and foregone payoff information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 50-72.
    9. Spenkuch, Jörg, 2014. "Backward Induction in the Wild: Evidence from the U.S. Senate," MPRA Paper 58766, University Library of Munich, Germany.
    10. Brosig-Koch, Jeannette & Heinrich, Timo & Helbach, Christoph, 2015. "Exploring the capability to reason backwards: An experimental study with children, adolescents, and young adults," European Economic Review, Elsevier, vol. 74(C), pages 286-302.
    11. Jeannette Brosig-Koch & Timo Heinrich & Christoph Helbach, 2012. "Exploring the Capability to Backward Induct – An Experimental Study with Children and Young Adults," Ruhr Economic Papers 0360, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    12. Brosig-Koch, Jeannette & Heinrich, Timo & Helbach, Christoph, 2014. "Does truth win when teams reason strategically?," Economics Letters, Elsevier, vol. 123(1), pages 86-89.
    13. Dasgupta Utteeyo, 2011. "Nudging Students Forward Towards Backward Induction," Journal of Industrial Organization Education, De Gruyter, vol. 5(1), pages 1-6, March.
    14. McKinney, C. Nicholas & Van Huyck, John B., 2021. "Does Playing Against An Error Prone Opponent Influence Learning in Nim?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 95(C).
    15. William Neilson & Michael Price & Mikhael Shor, 2016. "Nudging Backward Induction," Working papers 2016-31, University of Connecticut, Department of Economics.
    16. repec:zbw:rwirep:0360 is not listed on IDEAS
    17. McKinney, C. Nicholas & Van Huyck, John B., 2013. "Eureka Learning: Heuristics and response time in perfect information games," Games and Economic Behavior, Elsevier, vol. 79(C), pages 223-232.
    18. Gönül Doğan & Kenan Kalayci & Priscilla Man, 2024. "Pyramid Schemes," Discussion Papers Series 667, School of Economics, University of Queensland, Australia.
    19. Benito-Ostolaza, Juan M. & Hernández, Penélope & Sanchis-Llopis, Juan A., 2016. "Do individuals with higher cognitive ability play more strategically?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 5-11.
    20. Andreas Tutić & Sascha Grehl, 2017. "A Note on Disbelief in Others regarding Backward Induction," Games, MDPI, vol. 8(3), pages 1-7, August.
    21. 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.

    More about this item

    Keywords

    Nim game; incomplete information; subgame perfect Nash equilibrium; perfect Bayesian equilibrium; Fort Boyard.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ulp:sbbeta:2023-05. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.html .

    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.