We propose a class of multiple‐prior representations of preferences under ambiguity, where the belief the decision‐maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM's ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the co‐existence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual‐self expected utility (DSEU) , yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci (2004)), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler (1989)), while extensions of DSEU allow for more general departures from independence. We also provide foundations for a generalization of prior‐by‐prior belief updating to our model.

We propose non-parametric definitions of absolute and comparative naivete. These definitions leverage ex ante choice of menu to identify predictions of future behaviour and ex post (random) choices from menus to identify actual behaviour. The main advantage of our definitions is their independence from any assumed functional form for the utility function representing behaviour. An individual is sophisticated if she is indifferent ex ante between retaining the option to choose from a menu ex post or committing to her actual distribution of choices from that menu. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. We propose two definitions of comparative naivete and explore the restrictions implied by our definitions for several prominent models of time inconsistency.