• Set A of questions. For many years, the standard model of decision making has been the Expected Utility model. Its success rested on two main factors. First, its axiomatization seemed extremely appealing from a normative and, at first sight also descriptive, viewpoint. Second, in Economics and Finance applications, it turned out to be a rather easy to manage model, which allowed researchers to carry out meaningful comparative statics exercises. Nevertheless, after the famous thought experiments of Allais (1953) and Ellsberg (1961), the EU paradigm began to falter. In order to address the two different critiques of the EU model, and the mounting experimental evidence against it, a number of decision making models were then produced. The different proposed generalizations of EU can be roughly divided into two subgroups, which correspond to two different approaches to addressing agent’s violations of the EU paradigm: i) agents have incomplete preferences, ii) agents have complete preferences, but violate the key assumption defining EU, Independence.
- Are these two approaches connected and complementary?
- If so, are they capturing different aspects of the agent’s behavior?
- Can we also use this connection to measure how distant a model is from the EU paradigm?
- Can we interpret this latter measure as a measure of rationality of the agent?
These questions have been left, for the most part, unanswered. Only the first two have been partially addressed in the context of choice under ambiguity.2
• Set B of questions. The early success of the EU paradigm was further strengthened by the fact that, in a dynamic framework, recursivity of preferences turns out to coincide with Bayesian updating. On the other hand, most of the generalizations of the EU model were developed in a static setting, and very few were extended to a dynamic setting. These extensions are crucial for applications. A natural question is then:
- Can we provide a general foundation for recursive intertemporal preference models, under uncertainty, without relying on any speciÖcation of attitudes toward uncertainty?
• Set C of questions: One typical assumption in Economics is that agents make choices following a stable preference relation. This seems to be in contrast with the experimental evidence. Subjects, when asked to choose from the same set of options, often make different choices. One way to reconcile this evidence with the idea that an agent makes choices according to a stable preference. In this view, agents randomize their choices because they have an inherent preference for randomization. This interpretation is rather fascinating, particularly, from a theoretical perspective. In fact, preference for randomization has often been a key feature of models departing from the EU paradigm.
- Can we view stochastic choice as the result of rational behavior?
Another trait of the decision theoretic iterature that is noteworthy is the relative scarce number of applications, particularly, if the latter is compared to the size of the theoretical research produced.
- Can we provide applications to these models and ideas?
