Active learning with a misspecified prior

• 成果类型: Article
• 署名作者: Fudenberg, Drew; Romanyuk, Gleb; Strack, Philipp
• 署名单位: Massachusetts Institute of Technology (MIT); Harvard University; University of California System; University of California Berkeley
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1555-7561
• DOI: 10.3982/TE2480
• 发表日期: 2017-09-01
• 页码: 1155-1189
• 关键词: Active learning; learning in games; misspecified models

摘要

We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability 0 to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but unknown function of the action and an additive error term. We provide a complete characterization of asymptotic actions and beliefs when the agent's subjective state space is a doubleton. A simple example with three actions shows that in a misspecified environment a myopic agent's beliefs converge while a sufficiently patient agent's beliefs do not. This illustrates a novel interaction between misspecification and the agent's subjective discount rate.