Models of Subjective Learning
|Speaker:||David Dillenberger, University of Pennsylvania|
|Date:||Wednesday 2 November 2011|
We study a decision maker who faces a dynamic decision problem, in which the process of information arrival is subjective. By studying preferences over menus of acts, we derive a sequence of representations that capture the decision maker's un-certainty about the beliefs he will hold at the time of choosing from a menu. Our most general model is a model of second-order beliefs. We characterize a notion of "more preference for flexibility" via a subjective analogue of Blackwell's (1951, 1953) comparisons of experiments. We proceed to study a refined model in which signals are objectively describable as subsets of the state space. We provide a representation according to which the DM is only uncertain about the information set he will be in when choosing from the menu. We characterize the information systems that can support such a representation. The characterization is closely related to Shapley's (1967) notion of balanced weights. This representation has the advantage that, by introducing the comparative notion of "valuing binary bets more", we can describe how the behavior of two decision makers differs when one expects to learn more than the other, even if they do not agree on their prior beliefs. We then reinterpret the model in a way that allows us to study a decision maker who anticipates subjective uncertainty to be resolved gradually over time. We derive a representation that can be interpreted as follows: the decision maker holds beliefs over the states of the world and has in mind a filtration indexed by continuous time. Using Bayes' law, the filtration together with the beliefs generates a subjective temporal lottery. Both the filtration, which is the timing of information arrival and the sequence of partitions induced by it, and the beliefs, can be uniquely elicited from choice behavior. In this context, valuing binary bets more is equivalent to having a finer filtration. If two decision maker also share the same prior beliefs, then having a finer filtration is equivalent to having more preference for flexibility.