Nabil I. Al-Najjar

THE AMBIGUITY AVERSION LITERATURE: A CRITICAL ASSESSMENT

We provide a critical assessment of the ambiguity aversion literature, which we characterize in terms of the view that Ellsberg choices are rational responses to ambiguity, to be explained by relaxing Savages Sure-Thing principle and adding an ambiguity-aversion postulate. First, admitting Ellsberg choices as rational leads to behaviour, such as sensitivity to irrelevant sunk cost, or aversion to information, which most economists would consider absurd or irrational. Second, we argue that the mathematical objects referred to as “beliefs†in the ambiguity aversion literature have little to do with how an economist or game theorist understands and uses the concept. This is because of the lack of a useful notion of updating. Third, the anomaly of the Ellsberg choices can be explained simply and without tampering with the foundations of choice theory. These choices can arise when decision makers form heuristics that serve them well in real-life situations where odds are manipulable, and misapply them to experimental settings.

Aggregation and the law of large numbers in large economies

This paper introduces a new model of environments with a large number of agents and stochastic characteristics. We consider sequences of finite but increasingly large economies that ‘discretize’ the continuum. In the limit we obtain a model that is continuum-like in important respects, yet it has a countable set of agents with a finitely additive, ‘uniform’ distribution. In this model, the law of large numbers is meaningful and holds on all subintervals. This framework provides, among other things, a new interpretation of the measurability problem and the failure of the law of large numbers in the continuum. It is also shown that the Pettis integral in the continuum coincides with the empirical frequencies in the discrete model almost surely. Finally, the model is used to study a mechanism design problem in a large economy with private information.

Large Nonanonymous Repeated Games

Green, and later Sabourian studied repeated games where a player’s payoff depends on his actions and an anonymous aggregate outcome, and show that long-run players behave myopically in any equilibrium of such games. In this paper we extend these results to games where the aggregate outcome is not necessarily an anonymous function of players’ actions, and where players’ strategies may depend nonanonymously on signals of other players’ behavior. Our argument also provides a conceptually simpler proof of Green and Sabourian’s results, showing how their analysis is driven by general bounds on the number of pivotal players in a game.

Decision Makers as Statisticians: Diversity, Ambiguity, and Learning

I study individuals who use frequentist models to draw uniform inferences from independent and identically distributed data. The main contribution of this paper is to show that distinct models may be consistent with empirical evidence, even in the limit when data increases without bound. Decision makers may then hold different beliefs and interpret their environment differently even though they know each others model and base their inferences on the same evidence. The behavior modeled here is that of rational individuals confronting an environment in which learning is hard, rather than individuals beset by cognitive limitations or behavioral biases. Copyright 2009 The Econometric Society.

Strategically stable equilibria in games with infinitely many pure strategies

Abstract This paper studies the notion of Strategic Stability (Kohlberg and Mertens (Econometrica, 1986, 54, 1003–1039)) in games with compact metric spaces of pure strategies and continuous payoff functions. It is shown that stable sets exist and satisfy versions of the properties of admissibility, forward induction and elimination of dominated strategies.

Testing Theories with Learnable and Predictive Representations

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable prediction about future frequencies. We show that this test passes an expert who knows the data-generating process and cannot be manipulated by a uninformed one. Such a test is not possible if the theory is unrestricted.

Parametric representation of preferences

A preference is invariant with respect to a set of transformations if the ranking of acts is unaffected by reshuffling the states under these transformations. For example, transformations may correspond to the set of finite permutations, or the shift in a dynamic choice model. Our main result is that any invariant preference must be parametric: there is a unique sufficient set of parameters such that the preference ranks acts according to their expected utility given the parameters. Parameters are characterized in terms of objective frequencies, and can thus be interpreted as objective probabilities. By contrast, uncertainty about parameters is subjective. The preferences for which the above results hold are only required to be reflexive, transitive, monotone, continuous, and mixture linear.

Coarse decision making and overfitting

We study decision makers who willingly forgo decision rules that vary finely with available information, even though these decision rules are technologically feasible. We model this behavior as a consequence of using classical, frequentist methods to draw robust inferences from data. Coarse decision making then arises to mitigate the problem of over-fitting the data. The resulting behavior tends to be biased towards simplicity: decision makers choose models that are statistically simple, in a sense we make precise. In contrast to existing approaches, the key determinant of the level of coarsening is the amount of data available to the decision maker. The decision maker may choose a coarser decision rule as the stakes increase.

The Sunk Cost Bias and Managerial Pricing Practices

This paper provides an explanation for why the sunk cost bias persists among firms in a competitive environment in which rich learning possibilities are allowed. We envision firms that experiment with cost methodologies that are consistent with real-world accounting practices, including ones that confuse the relevance of variable, fixed, and sunk coststo pricing decisions. Firms follow “naive†adaptive learning to adjust prices and reinforcement learning to modify their costing methodologies. Costing and pricing practices that increase profits are reinforced. We show that all firms eventually display the sunk cost bias in their pricing behavior

On the Robustness of Factor Structures to Asset Repackaging

Abstract The paper provides a framework to study asset repackaging in a large asset economy, modeled as an atomless measure space of assets. The main theorem shows that, given an initial economy with strict factor space F , any economy obtained by repackaging these assets has a unique factor space F ′⊂ F . Thus, in contrast to earlier literature, factor structures are robust to the repackaging of asset.