Essays in Decision Theory

This dissertation studies decision theories for both individual and interactive choice problems. This thesis proposes three non-standard models that modify assumptions and settings of standard models. Chapter 1 provides an overview of this dissertation.

In the second chapter I present a model of decision-making under uncertainty in which an agent is constrained in her cognitive ability to consider complex acts. The complexity of an act is identified by the corresponding partition of state space. The agent ranks acts according to the expected utility net of complexity cost. I introduce a new axiom called Aversion to Complexity, that depicts an agent's aversion to complex acts. This axiom, together with other modified classical expected utility axioms characterizes a Complexity Aversion Representation. In addition, I present applications to competitive markets with uncertainty and optimal contract design.

The third Chapter discusses how a complexity averse agent measures the complexity cost of an act after she receives new information. I propose an updating rule for the complexity cost function called Minimal Complexity Updating. The idea is that if the agent is told that the true state must belong to a particular event, she needs not consider the complexity of an act outside of this event. The main result characterizes axiomatically the Minimal Complexity Aversion Representation. Lastly, I apply the idea of Minimal Complexity Updating to the theory of rational inattention.

The last chapter deals with a variant model of fictitious play, in which each player has a perturbation term that measures to what extent his rival will stick to the rules of traditional fictitious play. I find that the empirical distribution can converge to a pure Nash equilibrium if the perturbation term is bounded. Furthermore, I introduce an updating rule for the perturbation term. I prove that if the perturbation term is updated in accordance with this rule, then play can converge to a pure Nash equilibrium.