Browsing by Author "Sarver, Todd"

This dissertation consists of three essays in decision theory. The first chapter is an introduction. The second chapter studies individual decision making when deadlines are random. Since the quality of any decision relies on information and it takes time to gather information, a decision maker should have a preference over deadlines as well as over menus. Past research studies rationally inattentive decision making without deadlines. It is established that a decision maker’s informational constraint is revealed by her distaste for contingent planning. This paper extends the analysis to random deadlines and establishes the relationship between a decision maker’s preference over timed choice problems and the set of information acquisition paths she has available.

It is demonstrated that if a decision maker’s preference over random deadlines satisfies the von Neumann-Morgenstern independence axiom, then it is as if the decision maker’s optimal way to acquire information depends only on the menu she is presented with and is independent of the deadline. Moreover, if no information is lost along any path then the decision maker’s distaste for contingent planning becomes weaker as she is allowed more time to decide. The third chapter studies strategic situations where a population of heterogeneous players are randomly matched with each other to play games with strategic substitutes and players have incomplete information about their opponents' private types. If players hold type-independent beliefs about their opponents' types, then in equilibrium players' actions are monotonic with respect to their types. Since players' private types are often not observable to the analyst, to understand what kind of observable behavior can be explained by this model, a representation result is established for this model when the analyst observes how the population behaves on an aggregate level. Of course, a model with type-independent beliefs may not be justified, since types could be correlated in many applications. Moreover, in experiments where individuals are randomly matched to play games with strategic substitutes, they report systematically heterogeneous conjectures about their opponents' actions: Players who act more aggressively also conjecture that their opponents would act more aggressively. This not only contradicts the type-independent belief model, but is also counterintuitive because in games with strategic substitutes, opponents' aggressive behavior discourages players from playing aggressively. A model is then proposed where players have self-similar beliefs. It captures the intuition that higher types believe that their opponents are also of higher types and fits the experimental observations. One important and surprising result is that models with type-independent beliefs and self-similar beliefs are observationally equivalent for many payoff parameters, that is they have identical behavioral implications.

Decision problems could involve comparisons of alternatives according to different aspects. An alternative may be more desirable than another alternative in some of the aspects, yet less desirable in others. The multi-dimensional comparisons between alternatives requires a high degree of rationality -- the ability to make systematic trade-offs across aspects.

Limited ability to make such trade-offs could lead to the default bias, the tendency of choosing the default regardless of the presence of a better one. In dynamic decision problems, default bias causes a novel trade-off between the current consumption and the flexibility to switch in the future. An asset replacement problem and a contract design problem involving decision makers with default bias are studied.

A decision maker may resort to market information to better understand the right trade-off to make in multi-aspects comparisons between alternatives. When the market composition of products that features different aspects carry relevant information regarding the trade-offs, the decision maker’s choices between two products could be affected by the presence of other alternatives. Learning from markets explains violations of the properties of classic random utility maximization models.

Normatively appealing decision rules are proposed for each of the scenarios of multi-dimensional comparisons. A choice rule imposes behavioral conditions that the choice data must satisfy if the data is generated by such a rule. The essays in the dissertation identify the behavioral conditions that characterize the proposed choice rules: When the decision maker’s behaviors satisfy those conditions, the behaviors can be interpreted as if they are made according to the choice rule.

The dissertation distinguishes itself from some of the existing literature in that the set of attributes that a decision maker considers in her comparisons is not assumed to be observable. Instead, they can be uniquely identified from the choice behaviors. It extends the current understanding of some behavioral anomalies to a richer domain and proposes novel explanations of them.

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.