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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.20708 |
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| _version_ | 1866914113064534016 |
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| author | Esponda, Ignacio Pouzo, Demian |
| author_facet | Esponda, Ignacio Pouzo, Demian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Berk-Nash Rationalizability Esponda, Ignacio Pouzo, Demian Theoretical Economics Statistics Theory 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. |
| title | Berk-Nash Rationalizability |
| topic | Theoretical Economics Statistics Theory |
| url | https://arxiv.org/abs/2505.20708 |