A more robust definition of multiple priors∗

This paper provides a multiple-priors representation of ambiguous beliefs à la Ghirardato, Maccheroni, and Marinacci (2004) and Nehring (2002) for any preference that is (i) monotonic, (ii) Bernoullian, i.e. admits an affine utility representation when restricted to constant acts, and (iii) suitably continuous. Monotonicity is the main substantive assumption: we do not require either Certainty Independence or Uncertainty Aversion. We characterize the set of ambiguous beliefs in terms of Clarke-Rockafellar differentials. This allows us to provide an explicit calculation of the set of priors for several recent decision models: multiplier preferences, the smooth ambiguity model, the vector expected utility model, as well as confidence function, variational, general “uncertainty-averse” preferences, and mean-dispersion preferences. With an eye towards applications, our results indicate how assumptions about the individual’s perception of ambiguity translate to parametric restrictions in these functional representations. ∗We thank Simone Cerreia-Vioglio, Theo Diasakos, Fabio Maccheroni, Mark Machina, Pietro Ortoleva and Tomasz Strzalecki, as well as audiences at the 2009 RUD and SAET conferences, the Workshop in honor of Daniel Ellsberg (Vienna, May 2010), and at seminars in Rice, Northwestern, Penn, Princeton and Montreal for helpful comments. The usual disclaimer applies. Ghirardato is also grateful to the Italian MIUR for financial support. §DSMA and Collegio Carlo Alberto, Università di Torino; [email protected] ¶Northwestern University; [email protected]