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

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  • 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
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    File URL: http://beta.u-strasbg.fr/WP/2023/2023-05.pdf
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    References listed on IDEAS

    as
    1. Gisele Umbhauer, 2016. "Game theory and exercices [Théorie des jeux et exercices]," Post-Print hal-01762122, HAL.
    2. 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.
    3. 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.
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    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.

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    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

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