Belief Convergence under Misspecified Learning: A Martingale Approach
提出一种分析错误设定环境中学习结果的方法，引入“预测准确性”排序来部分恢复标准鞅收敛论证，推导出信念收敛的通用条件，并应用于慢学习环境，揭示微小错误设定可导致学习失败。
Abstract We present an approach to analyse learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e. from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously studied settings. Second, they enable us to analyse environments where learning is “slow”, such as costly information acquisition and sequential social learning. In such environments, we illustrate that even if agents learn the truth when they are correctly specified, vanishingly small amounts of misspecification can generate extreme failures of learning.