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Berk-Nash Rationalizability

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  • Ignacio Esponda
  • Demian Pouzo

Abstract

We study learning in complete-information games, allowing the players' models of their environment to be misspecified. We introduce Berk--Nash rationalizability: the largest self-justified set of actions -- meaning each action in the set is optimal under some belief that is a best fit to outcomes generated by joint play within the set. We show that, in a model where players learn from past actions, every action played (or approached) infinitely often lies in this set. When players have a correct model of their environment, Berk--Nash rationalizability refines (correlated) rationalizability and coincides with it in two-player games. The concept delivers predictions on long-run behavior regardless of whether actions converge or not, thereby providing a practical alternative to proving convergence or solving complex stochastic learning dynamics. For example, if the rationalizable set is a singleton, actions converge almost surely.

Suggested Citation

  • Ignacio Esponda & Demian Pouzo, 2025. "Berk-Nash Rationalizability," Papers 2505.20708, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2505.20708
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    References listed on IDEAS

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    1. Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
    2. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    3. 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.
    4. Kfir Eliaz & Ran Spiegler, 2020. "A Model of Competing Narratives," American Economic Review, American Economic Association, vol. 110(12), pages 3786-3816, December.
    5. 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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