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

Robert M. Anderson, Haosui Duanmu, Aniruddha Ghosh and M. Khan

Journal of Economic Theory, 2024, vol. 217, issue C

Abstract: 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 Berk-Nash 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 Esponda-Pouzo 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.

Keywords: Berk-Nash equilibrium; Markov decision process; Model misspecification; Learning (search for similar items in EconPapers)
JEL-codes: C02 C62 D01 D83 (search for similar items in EconPapers)
Date: 2024
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Working Paper: On Existence of Berk-Nash Equilibria in Misspecified Markov Decision Processes with Infinite Spaces (2023) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:217:y:2024:i:c:s002205312400019x

DOI: 10.1016/j.jet.2024.105813

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