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Higher-order learning

Author

Listed:
  • Piotr Evdokimov

    (Higher School of Economics)

  • Umberto Garfagnini

    (University of Surrey)

Abstract

We design a novel experiment to study how subjects update their beliefs about the beliefs of others. Three players receive sequential signals about an unknown state of the world. Player 1 reports her beliefs about the state; Player 2 simultaneously reports her beliefs about the beliefs of Player 1; Player 3 simultaneously reports her beliefs about the beliefs of Player 2. We say that beliefs exhibit higher-order learning if the beliefs of Player k about the beliefs of Player $$k-1$$ k - 1 become more accurate as more signals are observed. We find that some of the predicted dynamics of higher-order beliefs are reflected in the data; in particular, higher-order beliefs are updated more slowly with private than public information. However, higher-order learning fails even after a large number of signals is observed. We argue that this result is driven by base-rate neglect, heterogeneity in updating processes, and subjects’ failure to correctly take learning rules of others into account.

Suggested Citation

  • Piotr Evdokimov & Umberto Garfagnini, 2022. "Higher-order learning," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1234-1266, September.
    • Handle: RePEc:kap:expeco:v:25:y:2022:i:4:d:10.1007_s10683-021-09743-6
    DOI: 10.1007/s10683-021-09743-6
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    1. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    2. Angeletos, George-Marios & La’O, Jennifer, 2009. "Incomplete information, higher-order beliefs and price inertia," Journal of Monetary Economics, Elsevier, vol. 56(S), pages 19-37.
    3. , G. & , & ,, 2008. "Non-Bayesian updating: A theoretical framework," Theoretical Economics, Econometric Society, vol. 3(2), June.
    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. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    6. Holt, Charles A. & Smith, Angela M., 2009. "An update on Bayesian updating," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 125-134, February.
    7. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    8. J. M. Keynes, 1937. "The General Theory of Employment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 51(2), pages 209-223.
    9. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 729-762.
    10. Tanjim Hossain & Ryo Okui, 2013. "The Binarized Scoring Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 984-1001.
    11. 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.
    12. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Terri Kneeland, 2015. "Identifying Higher‐Order Rationality," Econometrica, Econometric Society, vol. 83(5), pages 2065-2079, September.
    14. ,, 2012. "A partial folk theorem for games with private learning," Theoretical Economics, Econometric Society, vol. 7(2), May.
    15. David M. Grether, 1980. "Bayes Rule as a Descriptive Model: The Representativeness Heuristic," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 537-557.
    16. Grether, David M., 1992. "Testing bayes rule and the representativeness heuristic: Some experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 17(1), pages 31-57, January.
    17. Yaron Azrieli & Christopher P. Chambers & Paul J. Healy, 2018. "Incentives in Experiments: A Theoretical Analysis," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1472-1503.
    18. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    19. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, May.
    20. David Danz & Lise Vesterlund & Alistair J. Wilson, 2020. "Belief Elicitation: Limiting Truth Telling with Information on Incentives," CESifo Working Paper Series 8048, CESifo.
    21. 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.
    22. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    23. 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.
    24. Huck, Steffen & Weizsacker, Georg, 2002. "Do players correctly estimate what others do? : Evidence of conservatism in beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 47(1), pages 71-85, January.
    25. , & , & ,, 2016. "Fragility of asymptotic agreement under Bayesian learning," Theoretical Economics, Econometric Society, vol. 11(1), January.
    26. Shane Frederick, 2005. "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, American Economic Association, vol. 19(4), pages 25-42, Fall.
    27. David Eil & Justin M. Rao, 2011. "The Good News-Bad News Effect: Asymmetric Processing of Objective Information about Yourself," American Economic Journal: Microeconomics, American Economic Association, vol. 3(2), pages 114-138, May.
    28. Stephen Morris & Hyun Song Shin, 2002. "Social Value of Public Information," American Economic Review, American Economic Association, vol. 92(5), pages 1521-1534, December.
    29. John Van Huyck & Ajalavat Viriyavipart & Alexander L. Brown, 2018. "When less information is good enough: experiments with global stag hunt games," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 527-548, September.
    30. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information," Econometrica, Econometric Society, vol. 72(5), pages 1583-1599, September.
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    More about this item

    Keywords

    Higher-order expectations; Learning; Theory of mind;
    All these keywords.

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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