On April 2nd, Raphaël Giraud (LED, Université Paris-VIII) is invited in the seminar of the team Décision, Rationalité, Interaction (IHPST) (from 5.00 to 7.00 pm, seminar room of the department of cognitive studies of École Normale Supérieure, 29 rue d’Ulm, 75005 Paris). The title of his presentation will be “An Elementary Axiomatization of the Smooth Ambiguity Model”.
Abstract: The smooth ambiguity model (Klibanoff, Marinacci, and Mukerji, 2005) is a growingly popular model of decision making under ambiguity among applied economists because it is very tractable compared to other alternatives. As far as its preference foundations are concerned, however, the situation is not entirely satisfactory: axiomatizations exist in the literature (Klibanoff et al., 2005; Nau, 2006; Seo, 2009; Giraud, 2014), yet none of them is set up in a framework that would make it directly comparable to the axiomatizations of alternative models. All extant axiomatizations use some form of enriched setup with respect to the traditional setup involving only first order acts (Savage acts or Anscombe-Aumann horse lotteries), they are not elementary. By contrast, we aim here at providing an elementary axiomatization of SOSEU, in the sense of only using first order acts. We show that the main axiom characterizing SOSEU in the class of preferences satisfying both continuity and the separation of utility from beliefs is a form of probability-wise dominance axiom with a twist capturing ambiguity attitude: given two portfolios of acts (i.e. weighted combinations of acts), if the weighted average of ambiguity-twisted expectations of each act in the first portfolio is larger than the corresponding weighted average of the second portfolio for all possible priors, then replacing the expectation by the certainty equivalent for each act in the portfolio does not reverse the preference. We also examine to what extent our axiomatization can be seen as a reduced form of other axiomatizations in the literature and prove that not all axiomatizations are equivalent, in the sense that Seo (2009)’s axiomatization uses the same amount of information as the one contained in our axiomatization, whereas Klibanoff et al. (2005)’s framework and axiomatization use extra and irreducible information.