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Active learning with a misspecified prior

Author

Listed:
  • Fudenberg, Drew

    (Department of Economics, Massachusetts Institute of Technology)

  • Romanyuk, Gleb

    (Department of Economics, Harvard University)

  • Strack, Philipp

    (Department of Economics, University of California Berkeley)

Abstract

We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability zero to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but unknown function of the action and an additive error term. We provide a complete characterization of asymptotic actions and beliefs when the agent's subjective state space is a doubleton. A simple example with three actions shows that in a misspecified environment a myopic agent's beliefs converge while a sufficiently patient agent's beliefs do not. This illustrates a novel interaction between misspecification and the agent's subjective discount rate.

Suggested Citation

  • Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
  • Handle: RePEc:the:publsh:2480
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    References listed on IDEAS

    as
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    Cited by:

    1. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.
    2. Takeshi Murooka & Yuichi Yamamoto, 2021. "Misspecified Bayesian Learning by Strategic Players: First-Order Misspecification and Higher-Order Misspecification," OSIPP Discussion Paper 21E008, Osaka School of International Public Policy, Osaka University.
    3. Zikai Xu, 2022. "Observational Learning with Competitive Prices," Papers 2202.06425, arXiv.org, revised May 2022.
    4. Hestermann, Nina & Le Yaouanq, Yves, 2018. "It\'s not my Fault! Self-Confidence and Experimentation," Rationality and Competition Discussion Paper Series 124, CRC TRR 190 Rationality and Competition.
    5. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R2, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    6. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    7. Aislinn Bohren & Daniel Hauser, 2018. "Social Learning with Model Misspeciification: A Framework and a Robustness Result," PIER Working Paper Archive 18-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jul 2018.
    8. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R2, Cowles Foundation for Research in Economics, Yale University, revised Oct 2021.
    9. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    10. Simone Cerreia-Vioglio & Lars Peter Hansen & Fabio Maccheroni & Massimo Marinacci, 2020. "Making Decisions under Model Misspecification," Papers 2008.01071, arXiv.org, revised Jun 2021.
    11. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Welfare Comparisons for Biased Learning," Cowles Foundation Discussion Papers 2274R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2021.
    12. Francis de Véricourt & Huseyin Gurkan, 2022. "Is your machine better than you? You may never know," ESMT Research Working Papers ESMT-22-02, ESMT European School of Management and Technology.
    13. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    14. José Luis Montiel Olea & Pietro Ortoleva & Mallesh Pai & Andrea Prat, 2021. "Competing Models," Working Papers 2021-89, Princeton University. Economics Department..
    15. Takeshi Murooka & Yuichi Yamamoto, 2021. "Multi-Player Bayesian Learning with Misspecified Models," OSIPP Discussion Paper 21E001, Osaka School of International Public Policy, Osaka University.
    16. Cuimin Ba, 2021. "Robust Model Misspecification and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Mar 2022.
    17. Else Gry Bro Christensen & Takeshi Murooka, 2020. "Procrastination and Learning about Self-Control," OSIPP Discussion Paper 20E001, Osaka School of International Public Policy, Osaka University.
    18. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    19. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    20. Kevin He & Jonathan Libgober, 2020. "Evolutionarily Stable (Mis)specifications: Theory and Applications," Papers 2012.15007, arXiv.org, revised Aug 2021.
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    22. Daniel Clark & Drew Fudenberg & Kevin He, 2022. "Observability, Dominance, and Induction in Learning Models," PIER Working Paper Archive 22-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    More about this item

    Keywords

    Active learning; learning in games; mis-specified models;
    All these keywords.

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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