We establish convergence of beliefs and actions in a class of one‐dimensional learning settings in which the agent's model is misspecified, she chooses actions endogenously, and the actions affect how she misinterprets information. Our stochastic‐approximation‐based methods rely on two crucial features: that the state and action spaces are continuous, and that the agent's posterior admits a one‐dimensional summary statistic. Through a basic model with a normal–normal updating structure and a generalization in which the agent's misinterpretation of information can depend on her current beliefs in a flexible way, we show that these features are compatible with a number of specifications of how exactly the agent updates. Applications of our framework include learning by a person who has an incorrect model of a technology she uses or is overconfident about herself, learning by a representative agent who may misunderstand macroeconomic outcomes, and learning by a firm that has an incorrect parametric model of demand.

中文翻译：

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错误指定学习模型的收敛

我们在一类一维学习环境中建立信念和行动的收敛，其中代理的模型被错误指定，她选择内生的行动，并且这些行动影响她如何误解信息。我们基于随机近似的方法依赖于两个关键特征：状态和动作空间是连续的，并且代理的后验接受一维汇总统计量。通过具有正常-正常更新结构的基本模型和代理对信息的误解可以灵活地依赖于她当前的信念的概括，我们表明这些特征与代理如何准确更新的许多规范兼容.