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A Theory of Updating Ambiguous Information

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  • Rui Tang

Abstract

We introduce a new updating rule, the conditional maximum likelihood rule (CML) for updating ambiguous information. The CML formula replaces the likelihood term in Bayes' rule with the maximal likelihood of the given signal conditional on the state. We show that CML satisfies a new axiom, increased sensitivity after updating, while other updating rules do not. With CML, a decision maker's posterior is unaffected by the order in which independent signals arrive. CML also accommodates recent experimental findings on updating signals of unknown accuracy and has simple predictions on learning with such signals. We show that an information designer can almost achieve her maximal payoff with a suitable ambiguous information structure whenever the agent updates according to CML.

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  • Rui Tang, 2020. "A Theory of Updating Ambiguous Information," Papers 2012.13650, arXiv.org.
  • Handle: RePEc:arx:papers:2012.13650
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    References listed on IDEAS

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    Cited by:

    1. Denis Shishkin & Pietro Ortoleva, 2021. "Ambiguous Information and Dilation: An Experiment," Working Papers 2020-53, Princeton University. Economics Department..
    2. Xiaoyu Cheng, 2020. "Ambiguous Persuasion under Dynamic Consistency," Papers 2010.05376, arXiv.org, revised Jul 2021.

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