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Ellsberg Behavior: a monotonicity consideration and its implications

Abstract

Consider a canonical problem in choice under uncertainty: choosing from a convex feasible set consisting of all (Anscombe-Aumann) mixtures of two acts f and g, \left\{ \alpha f+(1-\alpha)g:\alpha\in[0,1]\right\}. We propose a preference condition, Monotonicity in Mixtures, which says that clearly improving the act f (in the sense of weak dominance) makes putting more weight on f more desirable. We show that this property has strong implications for preferences exhibiting behavior as in the classic Ellsberg (1961) paradoxes. For example, we show that maxmin expected utility (MEU) preferences (Gilboa and Schmeidler 1989) satisfy Monotonicity in Mixtures if and only if they are expected utility preferences. Thus, for MEU, Monotonicity in Mixtures and Ellsberg behavior are incompatible. We extend this stark finding in several directions. Moreover, we demonstrate that the incompatibility is not between Monotonicity in Mixtures and Ellsberg behavior (or even global ambiguity aversion) per se. For example, in addition to deriving general implications of Monotonicity in Mixtures, we show that smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji 2005) can satisfy both properties as long as they are not too ambiguity averse. We discuss applications of our results to managerial decision making.

Type

Working Paper

Author(s)

Peter Klibanoff, Soheil Ghili

Date Published

2018

Citations

Klibanoff, Peter, and Soheil Ghili. 2018. Ellsberg Behavior: a monotonicity consideration and its implications.

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