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On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces

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  • Robert M. Anderson
  • Haosui Duanmu
  • Aniruddha Ghosh
  • M. Ali Khan

Abstract

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

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  • Robert M. Anderson & Haosui Duanmu & Aniruddha Ghosh & M. Ali Khan, 2022. "On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces," Papers 2206.08437, arXiv.org, revised Jul 2023.
  • Handle: RePEc:arx:papers:2206.08437
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    References listed on IDEAS

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    Cited by:

    1. Aniruddha Ghosh, 2024. "Robust Comparative Statics with Misspecified Bayesian Learning," Papers 2407.17037, arXiv.org.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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