Many violations of the Independence axiom of Expected Utility can be traced to subjects' attraction to risk-free prospects.Negative Certainty Independence, the key axiom in this paper, formalizes this tendency.Our main result is a utility representation of all preferences over monetary lotteries that satisfy Negative Certainty Independence together with basic rationality postulates.Such preferences can be represented as if the agent were unsure of how risk averse to be when evaluating a lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one.The set of utilities is unique in a well-defined sense.We show that our representation can also be derived from a 'cautious' completion of an incomplete preference relation.

We analyze a notion of self-confirming equilibrium with non-neutral ambiguity attitudes that generalizes the traditional concept. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is quite simple: by playing the same strategy in a stationary environment, an agent learns the implied distribution of payoffs, but alternative strategies yield payoffs with unknown distributions; increased aversion to ambiguity makes such strategies less appealing. In sum, a kind of “status quo bias” emerges; in the long run, the uncertainty related to tested strategies disappears, but the uncertainty implied by the untested ones does not.