Essays on Decision Theory

Abstract

This dissertation studies forward looking in dynamic choice. In the first chapter, we propose a dynamic choice model for an error-prone decision maker choosing among risky options. Our axioms yield a representation of the decision maker’s behavior in which the decision maker rationally anticipates her future mistakes, and might be averse to making choices. The resulting model provides a natural welfare criterion even though the decision maker makes mistakes. We introduce comparative measures of error-proneness and choice attitude. We characterize the logit quantal response model as a special case of our model that exhibits constant measure of error-proneness and choice neutrality. We show that different from standard risk, when risk is induced by mistakes, the expected value of a future decision problem might increase even if its options become worse.

In the second chapter, we dispense with the assumption of rational anticipation of future mistakes. We propose a model of backward induction with an error-prone decision maker who has limited understanding of her own future choices. To an outside observer, her behavior appears stochastic and her choices become imperfect signals of her payoffs. Our axioms yield a two-parameter representation of the decision maker’s behavior; one parameter characterizes her attitude towards complexity; i.e., her willingness to choose more complicated subtrees over simpler ones, the other her error-proneness. Our model nests fully rational backward induction as a limit of these parameters. We introduce and analyze a measure of complexity aversion and a measure of error-proneness. We show through examples how different decision trees induce different choice behavior in the context of product assortment and advertising problems.

In the last chapter, we present a negative result showing that if the forward looking satisfies three simple conditions, then the decision maker must have ignored her possible mistakes when looking forward. If one of the conditions, monotonicity is replaced with strict monotonicity, then forward looking can never satisfy all three conditions at the same time. We show in specific models of mistakes why these conditions are incompatible.