We find that Epstein (2010)'s Ellsberg-style thought experiments pose, contrary to his claims, no paradox or difficulty for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci and Mukerji (2005). Not only are the thought experiments naturally handled by the smooth ambiguity model, but our reanalysis shows that they highlight some of its strengths compared to models such as the maxmin expected utility model (Gilboa and Schmeidler, 1989). In particular, these examples pose no challenge to the model's foundations, interpretation of the model as affording a separation of ambiguity and ambiguity attitude or the potential for calibrating ambiguity attitude in the model.

This paper develops algorithms for dynamically consistent updating of ambiguous beliefs in the maxmin expected utility model of decision making under ambiguity. Dynamic consistency is the requirement that ex-ante contingent choices are respected by updated preferences. Such updating, in this context, implies dependence on the feasible set of payoff vectors available in the problem and/or on an ex-ante optimal act for the problem. Despite this complication, the algorithms are formulated concisely and are easy to implement, thus making dynamically consistent updating operational in the presence of ambiguity.

We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We first consider the definition proposed in Klibanoff, Marinacci, and Mukerji (2005) based on the classic Ellsberg two-urn paradox (Ellsberg (1961)), and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (1999), Epstein and Zhang (2001), Zhang (2002) and Ghirardato and Marinacci (2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (2001) and Zhang (2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (2001) and Zhang (2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.

This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition is applied to investigate some classes of preferences that allow for both independent randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a Savage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that CEU preferences that are uncertainty averse in the sense of Schmeidler should not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. Additionally, these points are used to reexamine some recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event.

We offer a theory of polarization as an optimal response to ambiguity. Suppose two individuals have different priors and individual A's beliefs first-order stochastically dominate individual B's. The individuals observe a common signal. Their beliefs exhibit polarization if individual A's posterior dominates her prior and individual B's prior dominates her posterior. We show a sense in which polarization is impossible under Bayesian updating and after the observation of extreme signals. However, we also show that polarization after observing an intermediate signal can arise from the efforts of ambiguity averse individuals to implement their optimal prediction strategies through dynamically consistent updating. When ambiguity averse individuals' beliefs are sufficiently close to opposite extremes, observing a neutral signal always leads to polarization. Under additional assumptions, we show that updating follows a threshold rule, allowing a more precise characterization of the conditions for polarization.

We define a behavioral concept of relevance in the context of decision making under uncertainty. We argue that this concept provides a sensible answer to the question "What probabilistic environments do an individual's preferences reveal as mattering to her decisions?" under a symmetry assumption. This question has important implications for economic modeling. It is often the case that a modeler desires to restrict the probabilistic environments a decision maker considers. Without a concept of relevant beliefs, it is impossible to check from preferences whether a model is reflecting what the modeler intended. This checking is essential to isolating the effect of changing information while holding tastes fixed. We show that a single concept of relevance delivers this for a wide range of models, including models that allow for ambiguity attitude. We also use symmetry and relevance to provide insight into the foundations of the α-MEU and smooth ambiguity models of decision-making under uncertainty

In this note, an $O ( | V |k )$ algorithm is described for determining whether an interval graph on $| V |$ vertices has a bandwidth less than or equal to a given integer $k$. While the algorithm is not the first to resolve this problem, it does admit a shorter proof of its correctness than a previous algorithm of the same complexity due to Kratsch (Information and Computation, 74 (1987), pp. 140–158)

The decision maker is in charge of procurement auctions at the department of transportation of Orangia (a fictitious U.S. state). Students are asked to assist him in estimating the winning bids in various auctions concerning highway repair jobs using data on past auctions. The decision maker is faced with various professional, statistical, and ethical dilemmas.

In Case (B) models for computing optimal bids in highway procurement auctions are developed from the perspective of the bidders.

An asset management company must replace the manager of its two signature mutual funds, who is about to retire. Two candidates have been short-listed. The management team is divided and cannot decide which of the two candidates would make the better mutual fund manager. The retiring manager presents a linear regression model to examine success factors of mutual fund managers. This linear regression is the starting point for the subsequent analysis.