Definitions of Ambiguous Events and the Smooth Ambiguity Model. - Klibanoff, P; Marinacci, M; Mukerji, S (Springer, 2011)
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 et al. (Econometrica 73(6):1849-1892, 2005) based on the classic Ellsberg two-urn paradox (Ellsberg Q J Econ 75:643-669, 1961) and show that it satisfies several desirable properties. We then compare this definition with those of Nehring (Math Soc Sci 38(2):197-213, 1999), Epstein and Zhang (Econometrica 69:265-306, 2001), Zhang (Econ Theory 20:159-181, 2002), and Ghirardato and Marinacci (J Econ Theory 102:251-289, 2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (J Econ Theory 102:251-289, 2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (Econometrica 69:265-306, 2001) and Zhang (Econ Theory 20:159-181, 2002) would yield a different classification. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (Econometrica 69:265-306, 2001) and Zhang (Econ Theory 20:159-181, 2002). The more interesting source is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.