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A sad lesson from the hammer-nail game: strength is better than dexterity

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  • Gisèle Umbhauer

Abstract

In this second paper on the hammer-nail game, we confront strength with dexterity. The hammer-nail game, a game played in the French TV show “Fort Boyard”, goes as follows: 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. A player is of non dexterity e if he is unable to hammer smoothly, so that, with one swing of the hammer, he drives the nail at least e millimeters into the support, with \uD835\uDC52 > 1. In a previous paper, we mainly studied the impact of strength, both players being of high dexterity (\uD835\uDC52 = 1), and we transformed the hammer-nail game into a Nim game with incomplete information on strength. In this paper we study the impact of both strength and dexterity. We confront two players of different strength and dexterity and namely show a sad result: strength is more useful than dexterity to win the game. We also study the behavior in front of incomplete information, either on strength or on dexterity.

Suggested Citation

  • 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.
    • Handle: RePEc:ulp:sbbeta:2023-31
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    File URL: http://beta.u-strasbg.fr/WP/2023/2023-31.pdf
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    References listed on IDEAS

    as
    1. 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.
    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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    More about this item

    Keywords

    Nim game; crossed cycles; Fort Boyard; subgame perfect Nash equilibrium; strength; dexterity; incomplete information; heuristics of behavior.;
    All these keywords.

    JEL classification:

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

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