We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a differential inclusion that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.

我们考虑一个通过可能错误指定的模型代表环境不确定性的代理商。在每个阶段，代理都会采取行动，观察结果，并使用贝叶斯规则来更新对环境的信念。该框架在经济学中正变得越来越流行，以研究由错误或有偏见的信念驱动的行为。通过首先表明预测代理人行为的关键因素是其过去行动的频率，我们能够根据描述行动频率演变的微分包含的解来表征一般情况下的渐近行为。然后，我们提出了一系列可以容易地应用于经济应用的含义，从而提供了可用于表征错误学习情况下行为的现成工具。