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Misspecified Beliefs about Time Lags

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  • Yingkai Li
  • Harry Pei

Abstract

We examine the long-term behavior of a Bayesian agent who has a misspecified belief about the time lag between actions and feedback, and learns about the payoff consequences of his actions over time. Misspecified beliefs about time lags result in attribution errors, which have no long-term effect when the agent's action converges, but can lead to arbitrarily large long-term inefficiencies when his action cycles. Our proof uses concentration inequalities to bound the frequency of action switches, which are useful to study learning problems with history dependence. We apply our methods to study a policy choice game between a policy-maker who has a correctly specified belief about the time lag and the public who has a misspecified belief.

Suggested Citation

  • Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    • Handle: RePEc:arx:papers:2012.07238
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    References listed on IDEAS

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    1. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    2. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    3. repec:dau:papers:123456789/184 is not listed on IDEAS
    4. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    5. Nyarko, Yaw, 1991. "Learning in mis-specified models and the possibility of cycles," Journal of Economic Theory, Elsevier, vol. 55(2), pages 416-427, December.
    6. Forges, Francoise, 1992. "Repeated games of incomplete information: Non-zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 6, pages 155-177, Elsevier.
    7. Philippe Jehiel & Larry Samuelson, 2012. "Reputation with Analogical Reasoning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(4), pages 1927-1969.
    8. Ran Spiegler, 2013. "Placebo Reforms," American Economic Review, American Economic Association, vol. 103(4), pages 1490-1506, June.
    9. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    10. Kfir Eliaz & Ran Spiegler, 2020. "A Model of Competing Narratives," American Economic Review, American Economic Association, vol. 110(12), pages 3786-3816, December.
    11. Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
    12. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    13. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    14. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Stability and Robustness in Misspecified Learning Models," Cowles Foundation Discussion Papers 2235, Cowles Foundation for Research in Economics, Yale University.
    15. He, Kevin, 2022. "Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems," Theoretical Economics, Econometric Society, vol. 17(3), July.
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    Cited by:

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    2. Bowen, T. Renee & Galperti, Simone & Dmitriev, Danil, 2021. "Learning from Shared News: When Abundant Information Leads to Belief Polarization," CEPR Discussion Papers 15789, C.E.P.R. Discussion Papers.

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