Updating Ambiguity Averse Preferences

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we charac- terize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As an appli- cation of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth am- biguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of Bayes's rule.Updating, Dynamic Consistency, Ambiguity, Regret, Ellsberg, Bayesian, Consequentialism, Smooth Ambiguity

Updating preferences with multiple priors

We propose and axiomatically characterize dynamically consistent update rules for decision making under ambiguity. These rules apply to the preferences with multiple priors of Gilboa and Schmeidler (1989), and are the first, for any model of preferences over acts, to be able to reconcile typical behavior in the face of ambiguity (as exemplified by Ellsberg’s paradox) with dynamic consistency for all non-null events. Updating takes the form of applying Bayes’ rule to subsets of the set of priors, where the specific subset depends on the preferences, the conditioning event, and the choice problem (i.e., a feasible set of acts together with an act chosen from that set).Updating, dynamic consistency, ambiguity, Ellsberg, Bayesian, consequentialism

Throughput Rate of a Two-worker Stochastic Bucket Brigade

Work-sharing in production systems is a modern approach that improves throughput rate. Work is shifted between cross-trained workers in order to better balance the material now in the system. When a serial system is concerned, a common work-sharing approach is the Bucket-Brigade (BB), by which downstream workers sequentially take over items from adjacent upstream work- ers. When the workers are located from slowest-to-fastest and their speeds are deterministic, it is known that the line does not suffer from blockage or starvation, and achieves the maximal theoretical throughput rate (TR). Very little is known in the literature on stochastic self-balancing systems with work-sharing, and on BB in particular. This paper studies the basic BB model of Bartholdi & Eisenstein (1996) under the assumption of stochastic worker speeds. We identify settings in which conclusions that emerge from deterministic analysis fail to hold when speeds are stochastic, in particular relating to worker order assignment as a function of the problem parameters

The ordinal Nash social welfare function

A social welfare function entitled [`]ordinal Nash' is proposed. It is based on risk preferences and assumes a common, worst social state (origin) for all individuals. The crucial axiom in the characterization of the function is a weak version of independence of irrelevant alternatives. This axiom considers relative risk positions with respect to the origin. Thus, the resulting social preference takes into account non-expected utility risk preference intensity by directly comparing certainty equivalent probabilities. The function provides an interpretation of the Nash-utility-product preference aggregation rule. Necessary and sufficient conditions for the function to produce complete and transitive binary relations are characterized.