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Beliefs and (In)Stability in Normal-Form Games

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  • Hyndman, Kyle
  • Terracol, Antoine
  • Vaksmann, Jonathan

Abstract

In this paper, we use experimental data to study players' stability in normal-form games where subjects have to report beliefs and to choose actions. Subjects saw each of 12 games four times in a regular or isomorphic form spread over two days without feedback. We document a high degree of stability within the same (strategically equivalent) game, although time and changes in the presentation of the game do lead to less stability. To look at stability across different games, we adopt the level-k theory, and show that stability of both beliefs and actions is significantly lower. Finally, we estimate a structural model in which players either apply a consistent level of reasoning across strategically different games, or reasoning levels change from game to game. Our results show that approximately 30% of subjects apply a consistent level of reasoning across the 12 games, but that they assign a low level of sophistication to their opponent. The remaining 70% apply different levels of reasoning to different games.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 47221.

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Date of creation: 23 May 2013
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Handle: RePEc:pra:mprapa:47221

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Keywords: Game theory; Beliefs; Stability; Level-$k$ thinking;

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References

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  1. Agranov, Marina & Potamites, Elizabeth & Schotter, Andrew & Tergiman, Chloe, 2012. "Beliefs and endogenous cognitive levels: An experimental study," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 449-463.
  2. Miguel Costa-Gomes & Vincent P. Crawford, 2004. "Cognition And Behavior In Two-Person Guessing Games: An Experimental Study," Levine's Bibliography, UCLA Department of Economics 122247000000000143, UCLA Department of Economics.
  3. Goeree, Jacob K. & Holt, Charles A., 2004. "A model of noisy introspection," Games and Economic Behavior, Elsevier, Elsevier, vol. 46(2), pages 365-382, February.
  4. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1329-1376, 09.
  5. Costa-Gomes, Miguel & Crawford, Vincent P. & Broseta, Bruno, 1998. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt1vn4h7x5, Department of Economics, UC San Diego.
  6. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer, Springer, vol. 15(4), pages 622-640, December.
  7. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, American Economic Association, vol. 85(5), pages 1313-26, December.
  8. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 119(3), pages 861-898, August.
  9. Dale O. Stahl & Paul W. Wilson, 2010. "On Players' Models of Other Players: Theory and Experimental Evidence," Levine's Working Paper Archive, David K. Levine 542, David K. Levine.
  10. Manski, Charles F., 2002. "Identification of decision rules in experiments on simple games of proposal and response," European Economic Review, Elsevier, Elsevier, vol. 46(4-5), pages 880-891, May.
  11. Miguel A. Costa-Gomes & Georg Weizs�cker, 2008. "Stated Beliefs and Play in Normal-Form Games," Review of Economic Studies, Oxford University Press, Oxford University Press, vol. 75(3), pages 729-762.
  12. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 25(3), pages 309-327, December.
  13. Trautmann, S.T. & Kuilen, G. van de, 2011. "Belief Elicitation: A Horse Race among Truth Serums," Discussion Paper, Tilburg University, Center for Economic Research 2011-117, Tilburg University, Center for Economic Research.
  14. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, American Economic Association, vol. 51(1), pages 5-62, March.
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Cited by:
  1. Heller, Yuval, 2012. "Three steps ahead," MPRA Paper, University Library of Munich, Germany 39429, University Library of Munich, Germany.

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