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Robust experimentation in the continuous time bandit problem

Farzad Pourbabaee ()
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Farzad Pourbabaee: University of California

Economic Theory, 2022, vol. 73, issue 1, No 5, 181 pages

Abstract: Abstract We study the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup (Bolton and Harris in Econometrica 67(2):349–374, 1999), where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences à la Hansen and Sargent (Am. Econ. Rev. 91(2):60–66, 2001), thus we frame the decision making environment as a two-player differential game against nature in continuous time. We characterize the DM’s value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. We then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, we show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion.

Keywords: Model uncertainty; Dynamic experimentation; Variational preferences; Information valuation; Ambiguous diffusion (search for similar items in EconPapers)
JEL-codes: C44 C61 C73 D81 D83 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00199-020-01328-3

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