This study of unawareness and ambiguity has three components. First, a model is development, where implicit information is embedded in the description of an act. For example, if a consumer is offered a warranty that provides $500 in case her tires disintegrate, she is made aware that such a contingency is possible. Given this recognition, the way a contract frames the states of the world becomes important. The model complements prospect theory, which considers the framing of consequences, by considering the framing of states. The choice objects of the model are lists of contingencies and payments.
This model provides two technical innovations to the theory of awareness. First, the decision maker's awareness is identified by her preferences over standard bets. Therefore, unawareness is associated with concepts of likelihood and probability rather than with knowledge and truth. This allows for partial awareness of her own unawareness. The explicit axiomatic approach also allows the analyst to predict how the decision maker will behave given a particular level of awareness from her preferences with other levels of awareness. Second, unawareness is defined over partitions of the entire state space, rather than over particular states. Then the decision maker can be aware of an event without being aware of its sub-events. For example, she can be aware that her transmission can fail, without listing all the specific components in her transmission that might break.
The second component of the study formulates a representation of ambiguity where the decision maker has a second order belief on the set of priors that is possibly nonlinearly aggregated. The existence of ambiguity is modeled by the spread of her second order belief while the attitude towards ambiguity is modeled by the curvature of the aggregator. Existing characterizations of this utility assume an exogenous product structure on the state space. For example, in a resent study, Klibanoff, Marinacci, and Mukerji assume that the second dimension of uncertainty is over the priors on the first dimension. This is especially troubling for providing f oundations, because the very concept of a prior is a decisional theoretical construct, like a discount factor or an Arrow-Pratt measure. This project attempts to disentangle the theory from such exogenous structure, identifying the representation from preference over direct bets on the states. An interesting procedure is presented for identifying the second order belief and the aggregator from first order preferences, which should yield a full characterization.
In the final part of the study, an experiment designed to estimate the parameters of this representation for ambiguity. It uses a novel graphical choice-theoretic design that provides enough data to confidently calibrate parameters, rather than simply test hypotheses. Such an estimate would be eminently useful in empirical applications.
The broader impact of this study is that both theories are especially conducive for applications. The model of unawareness developed here is constructed in the spirit of standard subjective models to facilitate its use. It keeps standard acts and contracts as its primitives. In fact, actual contracts are often communicated as lists of contingencies and payments. The representation of ambiguity allows separate comparative statics for the existence and aversion to ambiguity. Moreover, these comparative statics carry much of the intuition in standard risk theory. By providing foundations for such a representation, these techniques can be used confidently. In addition, the measurement device outlined here is of independent interest because it provides a general method to infer ambiguity aversion from a sparse amount of "local" data. The experimental calibration of ambiguity aversion provides a useful estimate to identify other empirical models that incorporate ambiguity aversion, in the same way that an estimate of the Arrow-Pratt measure helps to identify empirical models that incorporate risk aversion.
