Working Paper BETA #2023-16

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Title : The puzzling three-player beauty contest game: play 10 to win.

Author(s) : Gisèle Umbhauer

Abstract : In this paper, we study the 3-player beauty contest game. This 3-player guessing game has the same Nash equilibrium than the usual (large) N-player beauty contest game but it has also nice specific properties. To highlight these properties, we study classroom experiments on 2-player, 3-player and large N-player guessing games, both from a theoretical and behavioral point of view. The spirit of the paper is the spirit of the French newspaper Jeux et Stratégie which, in the early eighties, proposed the beauty contest game to his fun of logic readers. As a matter of facts, we wonder if it is possible to win the 3-player guessing game. So we show that, despite the 3-player beauty contest game has no weakly dominant strategy, it is possible to play it in a way that leads to win with a large probability, provided the parameter a is lower than 0.75. And we argue that playing 10 for a=0.6 ensures a large probability to win.

Key-words : beauty-contest game, 3-player game, guess, nombre d’or, dominance, win area, behavioral heuristic.

JEL Classification : C72, C9