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Ambiguity in the Small and in the Large
Author(s) -
Ghirardato Paolo,
Siniscalchi Marciano
Publication year - 2012
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta9367
Subject(s) - ambiguity aversion , ambiguity , prior probability , preference , lipschitz continuity , mathematical economics , monotonic function , preference relation , representation (politics) , independence (probability theory) , mathematics , affine transformation , knightian uncertainty , certainty , set (abstract data type) , econometrics , computer science , statistics , pure mathematics , bayesian probability , political science , mathematical analysis , geometry , politics , law , programming language
This paper considers local and global multiple‐prior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, that is, admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either certainty independence or uncertainty aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci's (2004) “unambiguous preference” relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of “locally better deviation” at an act and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.