Objective and Subjective Rationality in a Multiple Prior Model

I. GILBOA, F. Maccheroni, M. Marinacci, D. Schmeidler


March 2010, vol. 78, n°2, pp.755-770

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is "objectively rational" to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is "subjectively rational" to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation a la Bewley (2002) and a la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.Author Keywords: Multiple priors; rationality KeyWords Plus: UTILITY-THEORY; INCOMPLETE PREFERENCES; COMPLETENESS AXIOM; EXPECTED UTILITY; REPRESENTATION; AMBIGUITY; ATTITUDE; SPACES; RISK