Three Essays in Decision Theory

Abstract

This dissertation contributes to a few topics in decision theory including non-Bayesian updating, reference dependent choice, and limited attention. In the first chapter, I propose and axiomatically characterize a novel belief updating rule, called robust maximum likelihood updating, which can accommodate most commonly observed biases in probabilistic reasoning. In this updating rule, the decision maker is endowed with a benchmark prior, which is interpreted as the decision maker's "best guess," and a set of plausible priors. When the decision maker receives new information, she first revises her benchmark prior and then performs Bayesian updating based on the new benchmark prior. The revision of the benchmark prior is done in two stages. First, the decision maker restricts her attention to the subset of plausible priors which maximize the likelihood of the observed information. Next, the decision maker chooses a new prior within this set that is as "close" to the original benchmark prior as possible. The first stage reflects the decision maker's willingness to learn from the new information, and the second stage reflects her willingness to be as dynamically consistent as possible. I take the decision maker's preferences over acts (e.g., bets) before and after the arrival of new information as the primitive of analysis and propose axioms which characterize this updating rule. I show that the model provides explanations for confirmation bias, base rate neglect, conservatism bias and overconfidence. In the second chapter, I investigate choice behavior that differs from the standard rational choice model in two ways: (i) the decision maker's choices are reference dependent, and (ii) the decision maker pays attention to a subset of available alternatives. In this framework, I provide novel axiomatic characterizations of three commonly used random attention models: fixed independent consideration, logit consideration, fixed correlated consideration. While these models, or their variations, have been previously examined in the literature, the relationship between these models was not precisely known. My axiomatic characterization makes this relationship clear. First, I show that the fixed independent consideration model can be characterized by two key properties: irrelevance of dominated alternatives and ratio independence of dominant alternatives. Next, I show that logit consideration relaxes the former property while fixed correlated consideration relaxes the latter. Hence, the intersection of logit and fixed correlated consideration models is exactly fixed independent consideration. Finally, I illustrate how attention parameters can be (partially) recovered from observed choice behavior in all these models. In the third chapter which is coauthored with Yusufcan Masatlioglu, we study a model of search within a product network. A product network consists of a vast number of goods which are linked to one another. We investigate decision making in this new environment by using revealed preference techniques. In our model, the decision maker searches within the product network to uncover available goods. Due to the constraint imposed by the network structure and the starting point of search, the decision maker might not discover all available goods. We illustrate how one can deduce both the decision maker's preference and her product network from observed behavior. We also consider an extension of the model where the decision maker terminates the search before exhausting all the options (limited search).

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