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Information and Beliefs in a Repeated Normal-form Game

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  • Dietmar Fehr
  • Dorothea Kübler
  • David Danz

Abstract

We study beliefs and choices in a repeated normal-form game. In addition to a baseline treatment with common knowledge of the game structure, feedback about choices in the previous period and random matching, we run treatments (i) with fixed matching, (ii) without information about the opponent’s payoffs, and (iii) without feedback about previous play. Using Stahl and Wilson’s (1995) model of limited strategic reasoning, we classify behavior with regard to its strategic sophistication and consider its development over time. In the treatments with feedback and full information about the game, we observe more strategic play, more best-responses to beliefs and more accurate beliefs over time. While feedback is the main driving force of learning to play strategically and for forming beliefs that accurately predict the behavior of the opponent, both incomplete information about the opponent’s payoffs or lack of feedback lead to a stagnation of best-response rates over time. ZUSAMMENFASSUNG - (Information und Erwartungen in einem wiederholten Normalformspiel) Wir untersuchen die Entwicklung von den Erwartungen über das Verhalten des anderen Spielers und den Entscheidungen in einem wiederholten Normalformspiel. Zusätzlich zum Haupttreatment mit common knowledge über das Spiel, Feedback über das Ergebnis in der vorigen Runde und zufälliger Zuordnung der Spieler, gibt es Kontrolltreatments mit (i) festen paarweisen Zuordnungen der Spieler, (ii) ohne Information über die Auszahlungen des anderen Spielers und (iii) ohne Feedback über das Ergebnis der vorigen Runde. Mit Hilfe von Stahl und Wilsons (1995) Modell begrenzten strategischen Verhaltens klassifizieren wir das Verhalten der Teilnehmer im Hinblick auf die strategische Sophistikation. In den Treatments mit Feedback und vollständiger Information über das Spiel nehmen strategisches Verhalten, beste Antworten auf die eigenen Erwartungen und die Akkuratheit der Erwartungen über die Zeit zu. Während Feedback der Hauptgrund dafür ist, dass die Teilnehmer lernen, sich strategisch zu verhalten und korrekte Erwartungen über das Verhalten des anderen Spielers zu bilden, führen sowohl unvollständige Information über die Auszahlungen des Gegenspielers als auch fehlendes Feedback zu einer Stagnation der Rate der besten Antworten über die Zeit.

Suggested Citation

  • Dietmar Fehr & Dorothea Kübler & David Danz, 2010. "Information and Beliefs in a Repeated Normal-form Game," CIG Working Papers SP II 2010-02, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    • Handle: RePEc:wzb:wzebiv:fsiv2010-02
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    References listed on IDEAS

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    1. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    2. 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.
    3. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 729-762.
    4. Terracol, Antoine & Vaksmann, Jonathan, 2009. "Dumbing down rational players: Learning and teaching in an experimental game," Journal of Economic Behavior & Organization, Elsevier, vol. 70(1-2), pages 54-71, May.
    5. Asen Ivanov, "undated". "Strategic Play and Risk Aversion in One-Shot Normal-Form Games: An Experimental Study," Working Papers 0802, VCU School of Business, Department of Economics.
    6. David J. Cooper & John H. Kagel, 2005. "Are Two Heads Better Than One? Team versus Individual Play in Signaling Games," American Economic Review, American Economic Association, vol. 95(3), pages 477-509, June.
    7. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, vol. 46(2), pages 365-382, February.
    8. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    9. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 622-640, December.
    10. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    11. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    12. 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.
    13. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Review of Economic Studies, Oxford University Press, vol. 61(3), pages 567-588.
    14. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine.
    15. Pedro Rey Biel, 2005. "Equilibrium PLay and Best Response to (Stated) Beliefs in Constant Sum Games," Experimental 0506003, University Library of Munich, Germany.
    16. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    17. Clarke, Kevin A., 2007. "A Simple Distribution-Free Test for Nonnested Model Selection," Political Analysis, Cambridge University Press, vol. 15(3), pages 347-363, July.
    18. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 1998. "A theoretical analysis of altruism and decision error in public goods games," Journal of Public Economics, Elsevier, vol. 70(2), pages 297-323, November.
    19. Weber, Roberto A., 2003. "'Learning' with no feedback in a competitive guessing game," Games and Economic Behavior, Elsevier, vol. 44(1), pages 134-144, July.
    20. Oechssler, Jorg & Schipper, Burkhard, 2003. "Can you guess the game you are playing?," Games and Economic Behavior, Elsevier, vol. 43(1), pages 137-152, April.
    21. 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.
    22. Cox, James C. & Friedman, Daniel & Gjerstad, Steven, 2007. "A tractable model of reciprocity and fairness," Games and Economic Behavior, Elsevier, vol. 59(1), pages 17-45, April.
    23. Mariana Blanco & Dirk Engelmann & Alexander Koch & Hans-Theo Normann, 2010. "Belief elicitation in experiments: is there a hedging problem?," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 412-438, December.
    24. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    25. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    26. Kevin A. Clarke, 2003. "Nonparametric Model Discrimination in International Relations," Journal of Conflict Resolution, Peace Science Society (International), vol. 47(1), pages 72-93, February.
    27. Goeree, Jacob K. & Holt, Charles A. & Laury, Susan K., 2002. "Private costs and public benefits: unraveling the effects of altruism and noisy behavior," Journal of Public Economics, Elsevier, vol. 83(2), pages 255-276, February.
    28. Rick, Scott & Weber, Roberto A., 2010. "Meaningful learning and transfer of learning in games played repeatedly without feedback," Games and Economic Behavior, Elsevier, vol. 68(2), pages 716-730, March.
    29. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naivete, and Sophistication in Experimental Hide-and-Seek Games," Levine's Bibliography 321307000000000861, UCLA Department of Economics.
    30. Uri Gneezy, 2005. "Step-Level Reasoning and Bidding in Auctions," Management Science, INFORMS, vol. 51(11), pages 1633-1642, November.
    31. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    32. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
    33. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 861-898.
    34. Rutstrom, E. Elizabet & Wilcox, Nathaniel, 2008. "Stated versus inferred beliefs: A methodological inquiry and experimental test," MPRA Paper 11852, University Library of Munich, Germany.
    35. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 63-80.
    36. Anke Gerber, "undated". "Learning in and about Games," IEW - Working Papers 234, Institute for Empirical Research in Economics - University of Zurich.
    37. Kyle Hyndman & Erkut Y. Ozbay & Andrew Schotter & Wolf Ze’ev Ehrblatt, 2012. "Convergence: An Experimental Study Of Teaching And Learning In Repeated Games," Journal of the European Economic Association, European Economic Association, vol. 10(3), pages 573-604, May.
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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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