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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, as well as to represent context-dependent negative and positive ambiguity attitudes documented in experiments. We prove that our baseline representation, Boolean expected utility (BEU), 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 BEU allow for more general departures from independence.