# Essays on Decision Theory

Spring 5-15-2022

## Author's School

Graduate School of Arts and Sciences

Economics

## Degree Name

Doctor of Philosophy (PhD)

Dissertation

## Abstract

This dissertation provides three chapters on decision theory. The main purpose is to consider how economists can rationalize or explain the choices that are being made by decision makers in the economy. For example, when we observe certain substitution patterns among products in a market, we may be interested in questions like why such a pattern arises or what such behavior may tell us about substitution patterns among other similar products. Therefore, all of the chapters focus on writing mathematical models that can help explain the choice behaviors we may observe.The first two chapters focus mainly on what is sometimes referred to as random choice rules in the economic literature. The idea comes from the observation that the choice of an individual may change even when the set of options to choose from does not change. We develop models that can account for such randomness in choice. We capture some behavior that cannot be captured by some of the prevalent models from past literature such as the famous Random Utility Model. The general theme for the third chapter is the same, but we focus more on explaining why individuals may prefer certain sets of options over others. Again, the goal is to account for some complex behaviors that are more realistic than those of pre-existing literature.

In Chapter 1, we first propose a special case of the Random Utility Model that will address some of its problems. More specifically, the probability distribution over the strict total orders is unique and the axioms are simple. In addition to these properties, the model can easily be extended to a nested choice setting that allows us to be consistent with many observed behavioral phenomena. We axiomatically characterize the extension and show the parameters are identified. We then estimate the nested model on existing experimental data.

In Chapter 2, we introduce the notion of perception complementarity in a representation for random choice rules. We provide an axiomatic characterization and an identification result. Furthermore, we consider special cases of the model.

In Chapter 3, we provide an additive utility representation for complete and transitive preference over menus of alternatives. The representation makes it seem as if a sophisticated individual considers the state dependent payoffs of two individuals that must consume the same alternative from the menu. We also consider special cases of the model. We then find upper bounds on the minimal number of subjective states needed for the representation.

English (en)

## Chair and Committee

Jonathan Weinstein

David Ahn