Ambiguity in the Small and in the Large


  • Paolo Ghirardato,

    1. Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri (TO), Italy;
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  • Marciano Siniscalchi

    1. Economics Dept., Northwestern University, 2001 Sheridan Rd., Evanston, IL 60208, U.S.A.;
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    • We thank a co-editor and two anonymous referees, as well as Simone Cerreia-Vioglio, Theo Diasakos, Fabio Maccheroni, Mark Machina, Pietro Ortoleva, Daniele Pennesi, Tomasz Strzalecki, and audiences at the 2009 RUD and SAET conferences, the Workshop in honor of Daniel Ellsberg (Vienna, May 2010), and at seminars at Rice, Northwestern, Penn, Princeton, and Montreal for helpful comments. The usual disclaimer applies. Ghirardato is also grateful to the Italian MIUR for financial support. A version of Theorem 2 in this paper first appeared in the working paper “A More Robust Definition of Multiple Priors” (Ghirardato and Siniscalchi (2010)).


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.