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Robust experimentation in the continuous time bandit problem

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  • Farzad Pourbabaee

    (University of California)

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.

Suggested Citation

  • Farzad Pourbabaee, 2022. "Robust experimentation in the continuous time bandit problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 151-181, February.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:1:d:10.1007_s00199-020-01328-3
    DOI: 10.1007/s00199-020-01328-3
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    1. Matt Van Essen & John Wooders, 2023. "Dual auctions for assigning winners and compensating losers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1069-1114, November.
    2. Farzad Pourbabaee, 2024. "Reputation, learning and project choice in frictional economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1075-1115, December.

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    More about this item

    Keywords

    Model uncertainty; Dynamic experimentation; Variational preferences; Information valuation; Ambiguous diffusion;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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