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Rationalizability and Nash equilibria in guessing games

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  • Seel, Christian
  • Tsakas, Elias

Abstract

Games in which players aim to guess a fraction or multiple p of the average guess are known as guessing games or (p-)beauty contests. In this note, we derive a full characterization of the set of rationalizable strategies and the set of pure strategy Nash equilibria for such games as a function of the parameter p, the number of players and the (discrete) set of available guesses to each player.

Suggested Citation

  • Seel, Christian & Tsakas, Elias, 2017. "Rationalizability and Nash equilibria in guessing games," Games and Economic Behavior, Elsevier, vol. 106(C), pages 75-88.
    • Handle: RePEc:eee:gamebe:v:106:y:2017:i:c:p:75-88
    DOI: 10.1016/j.geb.2017.09.013
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    References listed on IDEAS

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    1. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    4. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    5. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    6. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    7. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    8. 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.
    9. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
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    Cited by:

    1. Carlos Alós-Ferrer & Johannes Buckenmaier, 2021. "Cognitive sophistication and deliberation times," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 558-592, June.

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    More about this item

    Keywords

    Guessing game; Beauty contest; Rationalizability;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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