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The ?-Beauty Contest: Choosing Numbers, Thinking Intervals

Author

Listed:
  • Enrico De Giorgi
  • Stefan Reimann

Abstract

The 1-shot ?-beauty contest is a non-equilibrium strategic game under bounded rationality conditions, while equilibrium is approached if the game is played iteratively sufficiently many times. Experimental data of the 1-shot setting of the 0-equilibrium game show a common pattern: The spectrum of announced numbers is a superposition of a skew background distribution and a regime of extra ordinarily often chosen numbers. Our model is capable of quantitatively reproducing this observation in non-equilibrium as well as the convergence towards equilibrium in the iterative setting. The approach is based on two basic assumptions: 1.) Players iteratively update their recent guesses in the sense of eductive reasoning and 2.) Players estimate intervals rather than exact numbers to cope with incomplete knowledge in non-equilibrium. The width of the interval is regarded as a measure for the confidence of the players' respective guess. It is shown analytically that the sequence of guessed numbers approaches a (finite) limit within only very few iterations. Moreover, if all players have infinite confidence in their respective guesses, the asymptotic Winning Number equals the rational Nash equilibrium 0, while if players have only finite confidence in their recent guess, the Winning Number in the 1-shot setting is strictly larger than 0. Our model is also capable of quantitatively describing the �path into equilibrium". Convergence is shown to be polynomial in the number of rounds played. The predictions of our model are in good quantitative agreement with real data for various ?-beauty contest games.

Suggested Citation

  • Enrico De Giorgi & Stefan Reimann, "undated". "The ?-Beauty Contest: Choosing Numbers, Thinking Intervals," IEW - Working Papers 183, Institute for Empirical Research in Economics - University of Zurich.
  • Handle: RePEc:zur:iewwpx:183
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    File URL: https://www.zora.uzh.ch/id/eprint/52079/1/iewwp183.pdf
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    References listed on IDEAS

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    1. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
    2. Falk Armin & Kosfeld Michael, 2012. "It's all about Connections: Evidence on Network Formation," Review of Network Economics, De Gruyter, vol. 11(3), pages 1-36, September.
    3. Ernst Fehr & Urs Fischbacher & Elena Tougareva, "undated". "Do High Stakes and Competition Undermine Fairness? Evidence from Russia," IEW - Working Papers 120, Institute for Empirical Research in Economics - University of Zurich.
    4. Stutzer, Alois, 2004. "The role of income aspirations in individual happiness," Journal of Economic Behavior & Organization, Elsevier, vol. 54(1), pages 89-109, May.
    5. Foellmi, Reto & Oechslin, Manuel, 2007. "Who gains from non-collusive corruption?," Journal of Development Economics, Elsevier, vol. 82(1), pages 95-119, January.
    6. Armin Falk & Andrea Ichino, "undated". "Clean Evidence on Peer Pressure," IEW - Working Papers 144, Institute for Empirical Research in Economics - University of Zurich.
    7. Falk, Armin & Lalive, Rafael & Zweimüller, Josef, 2005. "The success of job applications: a new approach to program evaluation," Labour Economics, Elsevier, vol. 12(6), pages 739-748, December.
    8. Armin Falk & Urs Fischbacher & Simon G�chter, "undated". "Living in Two Neighborhoods - Social Interactions in the Lab," IEW - Working Papers 150, Institute for Empirical Research in Economics - University of Zurich.
    9. Aleksander Berentsen & Guillaume Rocheteau & Shouyong Shi, 2007. "Friedman Meets Hosios: Efficiency in Search Models of Money," Economic Journal, Royal Economic Society, vol. 117(516), pages 174-195, January.
    10. Bruno Frey & Matthias Benz & Alois Stutzer, 2004. "Introducing Procedural Utility: Not Only What, but Also How Matters," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 160(3), pages 377-401, September.
    11. Frey, Bruno S. & Meier, Stephan, 2006. "The Economics of Museums," Handbook of the Economics of Art and Culture, in: V.A. Ginsburgh & D. Throsby (ed.), Handbook of the Economics of Art and Culture, edition 1, volume 1, chapter 29, pages 1017-1047, Elsevier.
    12. Fehr, Ernst & Henrich, Joseph, 2003. "Is Strong Reciprocity a Maladaptation? On the Evolutionary Foundations of Human Altruism," IZA Discussion Papers 712, Institute of Labor Economics (IZA).
    13. Bruno S. Frey & Simon Luechinger, "undated". "Terrorism: Deterrence May Backfire," IEW - Working Papers 136, Institute for Empirical Research in Economics - University of Zurich.
    14. Ernst Fehr & Urs Fischbacher & Bernhard von Rosenbladt & J�rgen Schupp & Gert G. Wagner, "undated". "A Nation-Wide Laboratory: Examining trust and trustworthiness by integrating behavioral experiments into representative surveys," IEW - Working Papers 141, Institute for Empirical Research in Economics - University of Zurich.
    15. Ernst Fehr & Jean-Robert Tyran, 2008. "Limited Rationality and Strategic Interaction: The Impact of the Strategic Environment on Nominal Inertia," Econometrica, Econometric Society, vol. 76(2), pages 353-394, March.
    16. Thorsten Hens & Klaus Reiner Schenk-Hoppé & Martin Stalder, 2002. "An Application of Evolutionary Finance to Firms Listed in the Swiss Market Index," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(IV), pages 465-487, December.
    17. Aleksander Berentsen, "undated". "Time-Consistent Private Supplie of Outside Paper Money," IEW - Working Papers 156, Institute for Empirical Research in Economics - University of Zurich.
    18. Berentsen Aleksander & Rocheteau Guillaume, 2003. "On the Friedman Rule in Search Models with Divisible Money," The B.E. Journal of Macroeconomics, De Gruyter, vol. 3(1), pages 1-21, December.
    19. Ernst Fehr & John A. List, 2004. "The Hidden Costs and Returns of Incentives-Trust and Trustworthiness Among CEOs," Journal of the European Economic Association, MIT Press, vol. 2(5), pages 743-771, September.
    20. Matthias Benz & Bruno S. Frey, 2008. "Being Independent is a Great Thing: Subjective Evaluations of Self‐Employment and Hierarchy," Economica, London School of Economics and Political Science, vol. 75(298), pages 362-383, May.
    21. 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.
    22. Bruno S. Frey & Simon Luechinger, "undated". "How to Fight Terrorism: Alternatives to Deterrence," IEW - Working Papers 137, Institute for Empirical Research in Economics - University of Zurich.
    23. Bruno S. Frey & Alois Stutzer, "undated". "Testing Theories of Happiness," IEW - Working Papers 147, Institute for Empirical Research in Economics - University of Zurich.
    24. Haim Levy & Enrico De Giorgi & Thorsten Hens, "undated". "Two Paradigms and Nobel Prizes in Economics: A Contradiction or Coexistence?," IEW - Working Papers 161, Institute for Empirical Research in Economics - University of Zurich.
    25. Haim Levy & Enrico De Giorgi & Thorsten Hens, "undated". "Prospect Theory and the CAPM: A contradiction or coexistence?," IEW - Working Papers 157, Institute for Empirical Research in Economics - University of Zurich.
    26. Enrico De Giorgi, "undated". "A Note on Portfolio Selection under Various Risk Measures," IEW - Working Papers 122, Institute for Empirical Research in Economics - University of Zurich.
    27. Foellmi, Reto & Zweimuller, Josef, 2004. "Inequality, market power, and product diversity," Economics Letters, Elsevier, vol. 82(1), pages 139-145, January.
    28. Michael Kosfeld, "undated". "Network Experiments," IEW - Working Papers 152, Institute for Empirical Research in Economics - University of Zurich.
    29. Bruno Frey & Stephan Meier, 2004. "In a field experiment," Natural Field Experiments 00243, The Field Experiments Website.
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    Cited by:

    1. Breitmoser, Yves, 2010. "Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games," MPRA Paper 19893, University Library of Munich, Germany.

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    More about this item

    Keywords

    Experiments; ?-Beauty Contest; Beliefs;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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