On existence of Berk-Nash equilibria in misspecified Markov decision processes with infinite spaces

• 成果类型: Article
• 署名作者: Anderson, Robert M.; Duanmu, Haosui; Ghosh, Aniruddha; Khan, M. Ali
• 署名单位: University of California System; University of California Berkeley; Harbin Institute of Technology; Johns Hopkins University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2024.105813
• 发表日期: 2024
• 关键词: Berk-Nash equilibrium; Markov Decision Process; Model Misspecification; learning

摘要

Model misspecification is a critical issue in many areas of economics. In the context of misspecified Markov Decision Processes, Esponda and Pouzo (2021) defined the notion of BerkNash equilibrium and established its existence with finite state and action spaces. However, many substantive applications (including two of the three motivating examples presented by Esponda and Pouzo) involve continuous state or action spaces, and are thus not covered by the EspondaPouzo existence theorem. We extend the existence of Berk-Nash equilibrium to compact action spaces and sigma -compact state spaces, with possibly unbounded utility functions. A complication arises because Berk-Nash equilibrium depends critically on Radon-Nikodym derivatives, which are bounded in the finite case but typically unbounded in misspecified continuous models. The proofs rely on nonstandard analysis, and draw on novel argumentation traceable to work of the second author on nonstandard representations of Markov processes.