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Static and Dynamic Decision Making under Uncertainty: Theory and Applications

Periodic Reporting for period 4 - SDDM-TEA (Static and Dynamic Decision Making under Uncertainty: Theory and Applications)

Reporting period: 2020-09-01 to 2021-08-31

• 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?
The team has been working on several projects connected to the initial ERC proposal.
1. In the paper “Deliberately Stochastic” joint with D. Dillenberger, P. Ortoleva, and G. Riella, we study whether and how choices that seem to be stochastic can be seen as the outcome of deliberate randomization. This project is connected to the questions in C.
2. In the paper “An Explicit Representation for Disappointment Aversion and Other Betweenness Preferences” joint with D. Dillenberger and P. Ortoleva. we study one of the most well-known models of non-expected utility: Gul (1991)’s model of Disappointment Aversion. This project is connected to the questions in D.
3. In the paper “Sources of Uncertainty and Subjective Prices” joint with V. Cappelli, F. Maccheroni, M. Marinacci, and S. Minardi, we develop a general framework to study source-dependent preferences in economic contexts. This project is connected to the questions in A.
4. In the paper “Multinomial logit processes and preference discovery” joint with F. Maccheroni, M. Marinacci, and A. Rustichini, we study and axiomatically characterize the dependence of choice probabilities on time in the softmax). This project is connected to the questions in C.
5. In the paper “A Canon of Probabilistic Rationality” joint with S. Cerreia-Vioglio, P. O. Lindberg, Fabio Maccheroni, Massimo Marinacci, and A. Rustichini, we show how an important property of stochastic choice, if satisfied, makes random choices of agents the result of a tie breaking rule among optimal alternatives. This project is connected to the questions in C.
6. In the paper “Absolute and Relative Ambiguity Aversion: A Preferential Approach” joint with F. Maccheroni, and M. Marinacci, we provide a framework to address how the uncertainty attitudes of a decision maker change while her wealth changes. .
7. In the paper “Making Decisions under Model Misspecification”, we use decision theory to confront uncertainty that is sufficiently broad to incorporate models as approximations.This project is connected to the questions in A.
8. In the paper Dynamic Opinion Aggregation: Long-run Stability and Disagreement joint with R. Corrao and G. Lanzani we propose a general model of social learning in networks that accounts for heuristics and biases in opinion aggregation. This project is connected to the questions in D.
All the projects mentioned have been described with their obtained outcomes and achieved goals. In terms of results achieved so far:
Paper 1 has been published in a “Top5” journal.
Paper 3 has been published in a “general audience” journal.
Papers 2, 5, and 6 have been published in “top field” journals in economics.
Papers 7 and 8 have been submitted to a “Top5” journal in economics.
Paper 4 is R&R in a Top 5 journal with a very favorable first round of reviews
The potential impact of the current research is big. Inter alia, the current research is truly interdisciplinary. More specifically:

Papers 1, 4, and 5 share a common theme: view the randomness of choices as a feature that is still compatible with the rationality of agents and not as a result of mistakes.
Paper 2 provides a novel take to an old and popular model opening new venues for its application in economics. Disappointment aversion seems to be a relevant feature of human behavior, but difficult to keep into account in the current version of the model. Our reformulation should allow researcher to introduce much more easily this behavioral aspect into their models.
Paper 6 provides an analysis that allows researchers to discuss wealth effects on uncertainty attitudes, which is tremendously important in economic applications. Before our work, there was no work formally addressing uncertainty aversion in connection to different wealth levels.
Paper 7 provides the first model of decision making under uncertainty which deals with concerns about model misspecification: something badly needed in economics applications. Before our work, there was no work on how incorporate model misspecification into decision criteria.
Paper 8 provides a completely novel approach to opinion aggregation on networks, which covers problems in the computer science literature as well as the economics one, with mathematical techniques which, to the best of our knowledge, are completely new for these fields.
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