Essays on Decision Theory and Information Economics

This dissertation consists of three chapters. Chapter one is a study in decision theory that analyzes regret and information avoidance. Chapter two is a study in information theory that characterizes the comparison of ambiguous information. Chapter three discusses a persuasion model with a constrained sender.

In chapter one, we study regret and information avoidance. Empirical evidence suggests that individuals selectively avoid information, depending on a relevant past choice or lack thereof. We address these findings by studying an agent whose choice behavior can be modeled as if she trades off two conflicting effects of information. The first is a psychological cost from the regret about past choices that are revealed to be suboptimal by the information, whereas the second is the instrumental value of information for making better-informed choices in the future. The primitive of our study is the agent's preference over pairs consisting of a set of menus and an information structure. A set of menus captures a three-period decision problem. Our main axioms reflect the agent's desire to limit her options in period one and to have more flexibility in period two. We posit axioms that connect the agent's consumption choice and information choice. A subjective version of the model is examined where the agent's information choice is not observable. We show that all parameters in both versions of the model can be uniquely identified from the choice behavior.

In chapter two, we study informativeness orders over ambiguous information structures. We generalize Blackwell (1951)'s informativeness order to ambiguous experiments. The ambiguity in experiments is rooted in a lack of understanding about their probabilistic content. Formally, an ambiguous experiment is modeled as a mapping from an auxiliary state space to the set of unambiguous experiments. We show that one ambiguous experiment is preferred to another by every decision maker for every decision problem if and only if they are related by a condition called prior-by-prior dominance, which states that for any first-order belief the decision maker entertains on the auxiliary state space, the expected experiment resulting from this belief for the first experiment is Blackwell more informative than that of the second. This equivalence is robust across a wide range of ambiguity preferences. Comparisons of sets of experiments evaluated using the maxmin criterion are studied as a special case and are shown to result in a weaker informativeness order called Wald-more-informative, which states that for any Blackwell experiment in the convex hull of the first set of experiments, there exists another in the convex hull of the second set that is Blackwell less informative.

In chapter three, we study a Bayesian persuasion problem where the persuader's choices of signals are constrained. Specifically, we model this constraint as an alpha-constraint: Probabilities of any signal realization being sent out conditional on any state of the world are bounded by alpha and one minus alpha. Under this constraint, we extend the revelation principle style result in persuasion games by showing that considering the signal realization space to be subsets of the action space is without loss of generality. But it is possible that recommending a proper subset of all actions is uniquely optimal. This possibility contrasts the existing result that having the signal realization space equal to the action space can always be optimal. Based on the revelation principle, we give an algorithm to solve the general constrained persuasion problems. We also provide a characterization of feasible distribution over posterior beliefs for the binary-state-binary-action case, and a comparison of the alpha-constraint and other existing constraints on the signal space.