Objective and Subjective Rationality in a Multiple Prior Model
Itzhak Gilboa, Fabio Maccheroni, Massimo Marinacci, David Schmeidler
Econometrica · 2010 · Volume 78 · Issue 2
Abstract
A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an “objective” sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a “subjective” sense: the DM cannot be convinced that she is wrong in making them. 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 choosefin the presence ofgif and only if the expected utility offis at least as high as that ofggiven each and every prior in the set. It is “subjectively rational” to choosefrather thangif and only if the minimal expected utility off(with respect to all priors in the set) is at least as high as that ofg. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à 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.
Keywords
Multiple priors, rationality
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