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Static and Dynamic Decision Making under Uncertainty: Theory and Applications

Periodic Reporting for period 3 - SDDM-TEA (Static and Dynamic Decision Making under Uncertainty: Theory and Applications)

Reporting period: 2019-03-01 to 2020-08-31

The team has been working on several projects connected to the initial ERC proposal: The first three are related to the expected utility paradigm. The last one, presents several applications.
First, the standard model of decision making in Economics has been for many years the Expected Utility (briefly, EU) model. However, experimental evidence suggests two potential critiques/violations of this model: either agents violate independence or they violate transitivity. These two are basic tenets underlying this model. The first principle amounts to assume that agents in evaluating alternatives, they evaluate them only on the part where they differ in the outcomes they yield. The second principle amounts to impose that agents who declare option a, preferred to option b, preferred to option c, will also declare a preferred to c. In order to cope with the aforementioned empirical evidence, economists suggested several alternative and more general models of decision making. These generalizations can be roughly divided into two subgroups, which correspond to two different approaches of addressing agents’ violations of the EU paradigm: i) agents have incomplete preferences, ii) agents have complete preferences, but violate the key assumptions that define EU: namely independence and/or transitivity. The first approach is more normative and maintains the view that the axioms defining EU are all appealing and rational, with the only exception of completeness of preferences (which amounts to say that an agent is always able to rank alternatives and can never be agnostic). The second approach is probably the most followed and it takes a more descriptive stance. In the paper “The Rational Core of Preference Relations” joint with E. A. Ok, we develop the notion of rationality core for a problem of choice under uncertainty. We show that any preference relation arising from the second approach can be seen as a completion of a preference relation coming from the first approach. In this way, we connect the two approaches and show that they are complementary. In other words, they are not two different views on human behavior, but rather two sides of the same coin. Moreover, we isolate a novel channel from where violations of the EU model might come from, namely, from a completion procedure.
Second, a typical assumption in Economics is that agents make choices following a stable preference relation. However, experimental evidence suggests that 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 relation is to consider agents randomize their choices because they have an inherent preference for randomization, as proposed by Machina (1985). 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. In the context of choice under risk, as shown by Cerreia-Vioglio, Dillenberger, and Ortoleva (2015), it is strictly related to the certainty effect namely, the phenomenon by which agents violate EU since they tend to favor risk-free options. In light of these observations, in the paper “Deliberately Stochastic” joint with D. Dillenberger and P. Ortoleva, we study stochastic choice as the outcome of deliberate randomization. First, we derive a general representation of a stochastic choice function with such property. Then, we proceed to characterize a model in which the agent has preferences over alternatives, and the stochastic choice is the optimal mix among available options. This model links stochasticity of choice and the phenomenon of certainty bias, with both behaviors stemming from the same source: multiple preferences and caution. We show that this model is behaviorally distinct from models of random utility used in the literature.
Third, 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 (or Multinomial Logit Process). MLP is the most widely used model of preference discovery in all fields of decision making from Quantal Response Equilibria to Discrete Choice Analysis, from Psychophysics to Combinatorial Optimization. Our axiomatic characterization of softmax permits to understand its conceptual underpinnings as a theory of agents’ behavior, as well as to empirically test its descriptive validity
All these projects have the aspiration of being foundational and help Economics researchers to use more realistic models of decision making. This is important in that the vast majority of economic models are microfounded meaning that they take individuals and their behavior as the basic unit. These models are also used in institutions that affect everyone’s life on a daily basis (e.g. central banks). Having more realistic models of human behavior not only can sharpen the predictions of models for a single decision, but also of models which describe the economy as an aggregation of human behaviors.
The potential impact of the current research is big. Inter alia, the current research is truly interdisciplinary as it covers several areas of human knowledge such as: Economics, Neuroscience, and Math. We were able to develop a notion of rational core of preferences which appears to be flexible and useful to economists, we were able to show that indeed a possibility why agents tend not to make the same choices in similar problems might be indeed due to a preference for diversification, and finally we were able to develop axiomatic characterizations for one of the most used models in Economics when stochastic choice is considered. This would allow for the possibility of easily validating or falsifying such theory within any data set. Finally, many of the scientific papers connected to the three above projects have been published in prestigious outlet certifying the aforementioned results.
From now, until the end of the project, we plan to expand on the aforementioned findings. For example, we aim to add time to our analysis. Most of the analysis we discussed until now has been carried out in a static framework, but clearly many relevant decisions involving human behavior bear fruit as time progresses. This is a difficult task. Indeed, despite a lot of work is present for static decisions very little has been done in intertemporal settings in considering departures from the EU paradigm.