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

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  • 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.

Suggested Citation

  • Gisèle Umbhauer, 2023. "The puzzling three-player beauty contest game: play 10 to win," Working Papers of BETA 2023-16, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2023-16
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    File URL: http://beta.u-strasbg.fr/WP/2023/2023-16.pdf
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    References listed on IDEAS

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    1. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
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    3. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
    4. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    5. Breitmoser, Yves, 2012. "Strategic reasoning in p-beauty contests," Games and Economic Behavior, Elsevier, vol. 75(2), pages 555-569.
    6. Grosskopf, Brit & Nagel, Rosemarie, 2008. "The two-person beauty contest," Games and Economic Behavior, Elsevier, vol. 62(1), pages 93-99, January.
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    More about this item

    Keywords

    beauty-contest game; 3-player game; guess; nombre d’or; dominance; win area; behavioral heuristic.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments

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