IDEAS home Printed from https://ideas.repec.org/a/kap/expeco/v13y2010i4p461-475.html
   My bibliography  Save this article

A finite mixture analysis of beauty-contest data using generalized beta distributions

Author

Listed:
  • Antoni Bosch-Domènech
  • José Montalvo
  • Rosemarie Nagel
  • Albert Satorra

Abstract

This paper introduces a mixture model based on the beta distribution, without preestablished means and variances, to analyze a large set of Beauty-Contest data obtained from diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a better t of the experimental data, and more precision to the hypothesis that a large proportion of individuals follow a common pattern of reasoning, described as iterated best reply (degenerate), than mixture models based on the normal distribution. The analysis shows that the means of the distributions across the groups of experiments are pretty stable, while the proportions of choices at di erent levels of reasoning vary across groups.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Antoni Bosch-Domènech & José Montalvo & Rosemarie Nagel & Albert Satorra, 2010. "A finite mixture analysis of beauty-contest data using generalized beta distributions," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 461-475, December.
    • Handle: RePEc:kap:expeco:v:13:y:2010:i:4:p:461-475
    DOI: 10.1007/s10683-010-9251-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10683-010-9251-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10683-010-9251-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Steffen Andersen & Glenn Harrison & Arne Hole & Morten Lau & E. Rutström, 2012. "Non-linear mixed logit," Theory and Decision, Springer, vol. 73(1), pages 77-96, July.
    3. Glenn W. Harrison & John A. List, 2004. "Field Experiments," Journal of Economic Literature, American Economic Association, vol. 42(4), pages 1009-1055, December.
    4. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    5. Andersen, Steffen & Harrison, Glenn W. & Hole, Arne Risa & Rutström, Elisabet E., 2009. "Non-Linear Mixed Logit and the Characterization of Individual Heterogeneity," Working Papers 06-2009, Copenhagen Business School, Department of Economics.
    6. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    7. Samuel Dastrup & Rachel Hartshorn & James McDonald, 2007. "The impact of taxes and transfer payments on the distribution of income: A parametric comparison," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 353-369, December.
    8. Peter Arcidiacono & John Bailey Jones, 2003. "Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm," Econometrica, Econometric Society, vol. 71(3), pages 933-946, May.
    9. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    10. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    11. Bognanno, Michael L, 2001. "Corporate Tournaments," Journal of Labor Economics, University of Chicago Press, vol. 19(2), pages 290-315, April.
    12. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    13. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    14. Colin Camerer & Teck-Hua Ho & Juin Kuan Chong, 2003. "A cognitive hierarchy theory of one-shot games: Some preliminary results," Levine's Bibliography 506439000000000495, UCLA Department of Economics.
    15. Heckman, James J & Willis, Robert J, 1977. "A Beta-logistic Model for the Analysis of Sequential Labor Force Participation by Married Women," Journal of Political Economy, University of Chicago Press, vol. 85(1), pages 27-58, February.
    16. Glenn Harrison & E. Rutström, 2009. "Expected utility theory and prospect theory: one wedding and a decent funeral," Experimental Economics, Springer;Economic Science Association, vol. 12(2), pages 133-158, June.
    17. Stahl, Dale O., 1998. "Is step-j thinking an arbitrary modelling restriction or a fact of human nature?," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 33-51, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hanaki, Nobuyuki & Koriyama, Yukio & Sutan, Angela & Willinger, Marc, 2019. "The strategic environment effect in beauty contest games," Games and Economic Behavior, Elsevier, vol. 113(C), pages 587-610.
    2. Francesco Fallucchi & Andrea Mercatanti & Jan Niederreiter, 2021. "Identifying types in contest experiments," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 39-61, March.
    3. Chen, Xiaohong & Ponomareva, Maria & Tamer, Elie, 2014. "Likelihood inference in some finite mixture models," Journal of Econometrics, Elsevier, vol. 182(1), pages 87-99.
    4. 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.
    5. Engel, Christoph, 2020. "Estimating heterogeneous reactions to experimental treatments," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 124-147.
    6. Mariano Runco, 2013. "Estimating depth of reasoning in a repeated guessing game with no feedback," Experimental Economics, Springer;Economic Science Association, vol. 16(3), pages 402-413, September.
    7. Chen, Xiao & Feng, Zhenghui & Peng, Heng, 2023. "Estimation and order selection for multivariate exponential power mixture models," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    8. Peter G Moffatt & Ganna Pogrebna & Graciela Zevallos-Porles, 2020. "Depth of Reasoning Models with Sophisticated Agents," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 20-06, School of Economics, University of East Anglia, Norwich, UK..
    9. Timo Ehrig & Jaison Manjaly & Aditya Singh & Shyam Sunder, 2022. "Adaptive Rationality in Strategic Interaction: Do Emotions Regulate Thinking About Others?," Strategy Science, INFORMS, vol. 7(4), pages 330-349, December.
    10. King King Li & Kang Rong, 2023. "A Two-Step Guessing Game," Post-Print hal-04376266, HAL.
    11. Burchardi, Konrad B. & Penczynski, Stefan P., 2014. "Out of your mind: Eliciting individual reasoning in one shot games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 39-57.
    12. Mariano Runco, 2015. "Bounded Rationality in a Cournot Duopoly Game," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 79-94, November.
    13. Johannes Leder & Leonhard Schilbach & Andreas Mojzisch, 2016. "Strategic Decision-Making and Social Skills: Integrating Behavioral Economics and Social Cognition Research," IJFS, MDPI, vol. 4(4), pages 1-14, November.
    14. Wengström, Erik, 2007. "Setting the Anchor: Price Competition, Level-n Theory and Communication," Working Papers 2007:6, Lund University, Department of Economics.
    15. Leder, Johannes & Häusser, Jan Alexander & Mojzisch, Andreas, 2015. "Exploring the underpinnings of impaired strategic decision-making under stress," Journal of Economic Psychology, Elsevier, vol. 49(C), pages 133-140.
    16. Müller, Julia & Schwieren, Christiane, 2011. "More than Meets the Eye: an Eye-tracking Experiment on the Beauty Contest Game," Working Papers 0516, University of Heidelberg, Department of Economics.
    17. King King Li & Kang Rong, 2024. "A two-step guessing game," Theory and Decision, Springer, vol. 97(1), pages 89-108, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    3. 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.
    4. Breitmoser, Yves, 2012. "Strategic reasoning in p-beauty contests," Games and Economic Behavior, Elsevier, vol. 75(2), pages 555-569.
    5. Dan Levin & Luyao Zhang, 2022. "Bridging Level-K to Nash Equilibrium," Papers 2202.12292, arXiv.org, revised Feb 2022.
    6. Burnham, Terence C. & Cesarini, David & Wallace, Björn & Johannesson, Magnus & Lichtenstein, Paul, 2007. "Billiards and Brains: Cognitive Ability and Behavior in a p-Beauty Contest," SSE/EFI Working Paper Series in Economics and Finance 684, Stockholm School of Economics.
    7. Breitmoser, Yves, 2010. "Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games," MPRA Paper 19893, University Library of Munich, Germany.
    8. Teck-Hua Ho & So-Eun Park & Xuanming Su, 2021. "A Bayesian Level- k Model in n -Person Games," Management Science, INFORMS, vol. 67(3), pages 1622-1638, March.
    9. Sergeyev, Dmitriy & Iovino, Luigi, 2018. "Central Bank Balance Sheet Policies Without Rational Expectations," CEPR Discussion Papers 13100, C.E.P.R. Discussion Papers.
    10. Vincent P. Crawford & Nagore Iriberri, 2004. "Fatal Attraction: Focality, Naivete, and Sophistication in Experimental Hide-and-Seek Games," Levine's Bibliography 122247000000000316, UCLA Department of Economics.
    11. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    12. Shapiro, Dmitry & Shi, Xianwen & Zillante, Artie, 2014. "Level-k reasoning in a generalized beauty contest," Games and Economic Behavior, Elsevier, vol. 86(C), pages 308-329.
    13. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    14. Amegashie, J. Atsu & Cadsby, C. Bram & Song, Yang, 2007. "Competitive burnout: Theory and experimental evidence," Games and Economic Behavior, Elsevier, vol. 59(2), pages 213-239, May.
    15. Syngjoo Choi, 2012. "A cognitive hierarchy model of learning in networks," Review of Economic Design, Springer;Society for Economic Design, vol. 16(2), pages 215-250, September.
    16. Breitmoser, Yves & Tan, Jonathan H.W. & Zizzo, Daniel John, 2014. "On the beliefs off the path: Equilibrium refinement due to quantal response and level-k," Games and Economic Behavior, Elsevier, vol. 86(C), pages 102-125.
    17. Colin Camerer & Teck-Hua Ho & Juin Kuan Chong, 2003. "A cognitive hierarchy theory of one-shot games: Some preliminary results," Levine's Bibliography 506439000000000495, UCLA Department of Economics.
    18. Kirstein, Annette & Kirstein, Roland, 2004. "Less Rationality, More Efficiency: a Laboratory Experiment on "Lemon" Markets," CSLE Discussion Paper Series 2004-02, Saarland University, CSLE - Center for the Study of Law and Economics.
    19. Annette Kirstein & Roland Kirstein, 2007. "Iterative Reasoning in an Experimental "Lemons" Market," FEMM Working Papers 07014, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    20. Berger, Ulrich & De Silva, Hannelore & Fellner-Röhling, Gerlinde, 2016. "Cognitive hierarchies in the minimizer game," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 337-348.

    More about this item

    Keywords

    Beauty-contest experiments; Decision theory; Reasoning hierarchy; Finite mixture distribution; Beta distribution; EM algorithm; C14; C16; C72; C91; D03;
    All these keywords.

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:expeco:v:13:y:2010:i:4:p:461-475. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.