IDEAS home Printed from https://ideas.repec.org/p/wzb/wzebiv/fsiv2010-02.html
   My bibliography  Save this paper

Information and Beliefs in a Repeated Normal-form Game

Author

Listed:
  • 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
    Note: Paper only available in English
    as

    Download full text from publisher

    File URL: http://skylla.wz-berlin.de/pdf/2010/ii10-02.pdf
    File Function: Full text (original version)
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    5. 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.
    6. 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.
    7. 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.
    8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, vol. 46(2), pages 365-382, February.
    17. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    18. 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.
    19. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    20. 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.
    21. 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.
    22. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    23. 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.
    24. Pedro Rey Biel, 2005. "Equilibrium PLay and Best Response to (Stated) Beliefs in Constant Sum Games," Experimental 0506003, University Library of Munich, Germany.
    25. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    26. Clarke, Kevin A., 2007. "A Simple Distribution-Free Test for Nonnested Model Selection," Political Analysis, Cambridge University Press, vol. 15(03), pages 347-363, June.
    27. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
    28. 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.
    29. 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.
    30. 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.
    31. Rutstrom, E. Elizabet & Wilcox, Nathaniel, 2008. "Stated versus inferred beliefs: A methodological inquiry and experimental test," MPRA Paper 11852, University Library of Munich, Germany.
    32. 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.
    33. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 63-80.
    34. Michi Kandori, 2010. "Social Norms and Community Enforcement," Levine's Working Paper Archive 630, David K. Levine.
    35. Anke Gerber, "undated". "Learning in and about Games," IEW - Working Papers 234, Institute for Empirical Research in Economics - University of Zurich.
    36. 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.
    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. Sutter, Matthias & Czermak, Simon & Feri, Francesco, 2010. "Strategic Sophistication of Individuals and Teams in Experimental Normal-Form Games," IZA Discussion Papers 4732, Institute for the Study of Labor (IZA).
    2. 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.
    3. Hyndman, Kyle & Terracol, Antoine & Vaksmann, Jonathan, 2013. "Beliefs and (In)Stability in Normal-Form Games," MPRA Paper 47221, University Library of Munich, Germany.
    4. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    5. Nick Feltovich & Sobei H. Oda, 2014. "Special Section: Experiments on Learning, Methods, and Voting," Pacific Economic Review, Wiley Blackwell, vol. 19(3), pages 260-277, August.
    6. Evdokimov, Piotr & Rustichini, Aldo, 2016. "Forward induction: Thinking and behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 195-208.
    7. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    8. Florian Artinger & Filippos Exadaktylos & Hannes Koppel & Lauri Sääksvuori, 2010. "Applying Quadratic Scoring Rule transparently in multiple choice settings: A note," Jena Economic Research Papers 2010-021, Friedrich-Schiller-University Jena.
    9. Ozan Aksoy & Jeroen Weesie, 2013. "Hierarchical Bayesian Analysis of Biased Beliefs and Distributional Other-Regarding Preferences," Games, MDPI, Open Access Journal, vol. 4(1), pages 1-23, February.
    10. Dominik Bauer & Irenaeus Wolff, 2018. "Biases in Beliefs: Experimental Evidence," TWI Research Paper Series 109, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    11. Dorothea Kübler, 2010. "Experimental Practices in Economics: Performativity and the Creation of Phenomena," CIG Working Papers SP II 2010-01, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    12. Lindner, Florian & Sutter, Matthias, 2013. "Level-k reasoning and time pressure in the 11–20 money request game," Economics Letters, Elsevier, vol. 120(3), pages 542-545.
    13. Claudia Neri, 2015. "Eliciting beliefs in continuous-choice games: a double auction experiment," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 569-608, December.
    14. Czermak, Simon & Feri, Francesco & Glätzle-Rützler, Daniela & Sutter, Matthias, 2010. "Strategic Sophistication of Adolescents: Evidence from Experimental Normal-Form Games," IZA Discussion Papers 5049, Institute for the Study of Labor (IZA).
    15. Charness, Gary & Gneezy, Uri & Halladay, Brianna, 2016. "Experimental methods: Pay one or pay all," Journal of Economic Behavior & Organization, Elsevier, vol. 131(PA), pages 141-150.
    16. repec:kap:theord:v:82:y:2017:i:4:d:10.1007_s11238-016-9579-3 is not listed on IDEAS
    17. repec:eee:jeborg:v:150:y:2018:i:c:p:202-219 is not listed on IDEAS
    18. Jordi Brandts & David J. Cooper, 2015. "Centralized vs. Decentralized Management: an Experimental Study," Working Papers 854, Barcelona Graduate School of Economics.
    19. Flip Klijn & Marc Vorsatz, 2017. "Outsourcing with identical suppliers and shortest-first policy: a laboratory experiment," Theory and Decision, Springer, vol. 82(4), pages 597-615, April.
    20. Sutter, Matthias & Czermak, Simon & Feri, Francesco, 2013. "Strategic sophistication of individuals and teams. Experimental evidence," European Economic Review, Elsevier, vol. 64(C), pages 395-410.
    21. Czermak, Simon & Feri, Francesco & Glätzle-Rützler, Daniela & Sutter, Matthias, 2016. "How strategic are children and adolescents? Experimental evidence from normal-form games," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 265-285.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wzb:wzebiv:fsiv2010-02. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jennifer Rontganger). General contact details of provider: http://edirc.repec.org/data/cicwzde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.