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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

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    13. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised Nov 2019.
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    Citations

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    Cited by:

    1. 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.
    2. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    3. 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.
    4. Nina Hestermann & Yves Le Yaouanq, 2019. "It's not my Fault! Self-Confidence and Experimentation," CESifo Working Paper Series 7501, CESifo Group Munich.
    5. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    6. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128, Cowles Foundation for Research in Economics, Yale University.
    7. Mira Frick & Ryota Iijima & Yuhta Ishii, 2019. "Misinterpreting Others and the Fragility of Social Learning," Cowles Foundation Discussion Papers 2160, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Active learning; learning in games; mis-specified models;

    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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