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Limit Points of Endogenous Misspecified Learning

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  • Drew Fudenberg
  • Giacomo Lanzani
  • Philipp Strack

Abstract

We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

Suggested Citation

  • Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2021. "Limit Points of Endogenous Misspecified Learning," Econometrica, Econometric Society, vol. 89(3), pages 1065-1098, May.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:3:p:1065-1098
    DOI: 10.3982/ECTA18508
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    Cited by:

    1. Larry Samuelson & Jakub Steiner, 2024. "Constrained data-fitters," ECON - Working Papers 460, Department of Economics - University of Zurich.
    2. Yingkai Li & Argyris Oikonomou, 2024. "Dynamics and Contracts for an Agent with Misspecified Beliefs," Papers 2405.20423, arXiv.org.
    3. Yingkai Li & Aleksandrs Slivkins, 2022. "Exploration and Incentivizing Participation in Randomized Trials," Papers 2202.06191, arXiv.org, revised Mar 2025.
    4. Luca Braghieri, 2023. "Biased Decoding and the Foundations of Communication," CESifo Working Paper Series 10432, CESifo.
    5. In-Koo Cho & Jonathan Libgober, 2022. "Learning Underspecified Models," Papers 2207.10140, arXiv.org.
    6. Duarte Gonc{c}alves, 2022. "Sequential Sampling Equilibrium," Papers 2212.07725, arXiv.org, revised Nov 2023.
    7. Chen, Jaden Yang, 2022. "Biased learning under ambiguous information," Journal of Economic Theory, Elsevier, vol. 203(C).
    8. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    9. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. Anderson, Robert M. & Duanmu, Haosui & Ghosh, Aniruddha & Khan, M. Ali, 2024. "On existence of Berk-Nash equilibria in misspecified Markov decision processes with infinite spaces," Journal of Economic Theory, Elsevier, vol. 217(C).
    11. Ba, Cuimin & Gindin, Alice, 2023. "A multi-agent model of misspecified learning with overconfidence," Games and Economic Behavior, Elsevier, vol. 142(C), pages 315-338.

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