This paper identifies two distinct types of payoff kinks that can be exhibited by preference functions over monetary lotteries - "locally separable" vs. "locally nonseparable" - and illustrates their relationship to the payoff and probability derivatives of such functions. Expected utility and Fréchet differentiable preference functions are found to be incapable of exhibiting locally nonseparable payoff kinks; rank-dependent preference functions are incapable of avoiding them.

Robustify. To identify the analytical aspects of a model that continue to hold under more genral conditions. This usually requires expressing the model and its results in a particular manner as statements that may be logically equivalent under the assumptions of a given model can differ widely in their robustness to dropping these assumptions. E.g., "By expressing the classical expected utility/subjective probability model in event-theoretic therms, tis asic concepts, tools and results can be locally and globally robustified to general 'event-smooth' preferences over subjectively uncertain acts that do not necessarily exhibit either expected utility risk preferences or probabilistic beliefs."

Every subjective state space with sufficient (e.g., Euclidean) structure contains almost-objective events that approximate, and in the limit attain, the standard properties of objectively uncertain events for all individuals with event-smooth betting preferences - whether they are expected utility/non-expected utility, state-independent/state-dependent, or probabilistically sophisticated/non-probabilistically sophisticated. These properties include well-defined and unanimously agreed-upon revealed likelihoods that are independent of the realization of other subjective events, probabilistic sophistication over almost-objective acts, and linearity of state-independent or state-dependent expected utility preferences over almost-objective acts and almost-objective mixtures of subjective acts. Many real-world randomization devices are based on events of this form.

This dissertation contains three chapters, the first two of which are on decision theory and the last of which is on social and economic networks. In the first chapter, I model a decision maker who is able to evaluate the available options in multiple subjective dimensions or attributes, but is not generally able to aggregate the values of these attributes through a single utility function to rank the available options. This inability arises whenever there are multiple attributes that lead to conflicting ranking over the options. The model that I propose is able to account for a number of violations of standard utility maximization models such as stochastic choice and context dependence, in particular the attraction effect and the compromise effect. I provide an axiomatic characterization of my model. An important feature of this model is that attributes are identified through the observed choices.

The second chapter extends the random utility framework to the realm of choices over menus of alternatives. More specifically, I assume that as modelers we can only observe the aggregate choices of a heterogenous population of decision makers over menus (e.g. restaurants). Furthermore, I assume that each member of the population behaves according to the standard model of choice over menus. Specifically, each decision maker has a well-defined strict preference ordering over individual alternatives (e.g. meals) and chooses an available restaurant that offers the best meal among all the available restaurants. The potential heterogeneity of the population makes the aggregate choices over menus appear stochastic. In the main result of the paper, I provide a characterization of all stochastic choice data over menus that are consistent with a population of standard decision makers.

The third chapter is on social and economic networks and studies the integration of two communities that face a barrier to communicate with one another. We assume that nodes benefit from both direct and indirect connections, but direct connections come also with a cost. We capture the barrier of communication between the two communities by assuming that inter-community links are more costly than intra-community links. In this context, we characterize all integrated structures that are efficient. Next, we determine which of these efficient structures can be also stable. A notable feature of our work is a new class of multi core and periphery structures that we introduce in this paper as parallel hyperstars.

Many standard structural models in economics have the property that they induce persistent, partially predictable heteroskedasticity ("volatility clustering") in their key dependent variables, even when their underlying stochastic shock variables are all serially independent and homoskedastic, and their structural parameters are all time-invariant. This paper presents examples of this phenomenon, and examines the nature of such induced volatility clustering.