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Bayesian Learning When Players Are Misspecified about Others

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  • Takeshi Murooka
  • Yuichi Yamamoto

Abstract

This paper considers Bayesian learning when players are biased about the data-generating process, and are biased about the opponent’s bias about the data-generating process. Specifically, we assume that each player’s bias about others takes the form of interpersonal projection, which is a tendency to overestimate the extent to which others share the player’s own view. We show that even an arbitrarily small amount of bias can destroy correct learning of an unknown state, i.e., there is zero probability of the posterior belief staying in a neighborhood of the true state.

Suggested Citation

  • Takeshi Murooka & Yuichi Yamamoto, 2025. "Bayesian Learning When Players Are Misspecified about Others," ISER Discussion Paper 1284, Institute of Social and Economic Research, The University of Osaka.
    • Handle: RePEc:dpr:wpaper:1284
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    File URL: https://www.iser.osaka-u.ac.jp/static/resources/docs/dp/DP1284.pdf
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
    2. Tristan Gagnon-Bartsch & Antonio Rosato, 2024. "Quality Is in the Eye of the Beholder: Taste Projection in Markets with Observational Learning," American Economic Review, American Economic Association, vol. 114(11), pages 3746-3787, November.
    3. 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.
    4. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
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