Working Paper BETA #2023-31

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

Author(s) : 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.

Key-words : Nim game, crossed cycles, Fort Boyard, subgame perfect Nash equilibrium, strength, dexterity, incomplete information, heuristics of behavior.

JEL Classification : C72