Essays on Dynamic Decisions Under Uncertainty

Cheng, Xiaoyu

doi:https://doi.org/10.21985/n2-3qrr-4w37

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Essays on Dynamic Decisions Under Uncertainty

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This dissertation comprises three essays that study dynamic decisions under uncertainty--in particular, ambiguity. The first two chapters develop new decision models that emphasize the role of making statistical inferences in decisions. The third chapter highlights, in the context of persuasion, how different decision models can lead to distinct conclusions in economic models. In Chapter 1, I propose and axiomatize a new updating rule: Relative Maximum Likelihood (RML) updating for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear contraction of C towards its subset ascribing the maximal probability to the observed event. As a result, two well-known updating rules, full Bayesian (FB) and Maximum Likelihood (ML), are included as special cases of RML. The axiomatization relies on weakening the axioms characterizing FB and ML. The axiom characterizing ML is identified for the first time here, addressing a long-standing open question in the literature. In Chapter 2, I consider a decision environment where sample data are governed by an unknown sequence of independent but possibly non-identical distributions. In this case, the data-generating process (DGP) in general cannot be perfectly identified from the data. For making decisions facing such uncertainty, this chapter presents a novel approach by studying how the data can best be used to robustly improve decisions. That is, no matter which DGP governs the uncertainty, one can make a better decision than without using the data. I show that common inference methods, e.g., maximum likelihood and Bayesian updating cannot achieve this goal. To address, I develop new updating rules that lead to robustly better decisions either asymptotically almost surely or in finite sample with a pre-specified probability. The final chapter studies the question: in a persuasion game, if both the sender and receiver are ambiguity averse, can the sender benefit from sending ambiguous messages? I show that the sender cannot benefit if the receiver is dynamically consistent. However, if the sender is strictly less ambiguity averse than the receiver, then she may benefit even when facing a dynamically consistent receiver. This gain comes from extracting an ambiguity premium by exploiting the differences in the ambiguity attitudes.

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