Discovery and Dynamic Consistency

Abstract

We provide a simple model in which the decision maker successively discovers elements of the world and expands the state space over time. We propose a dynamic consistency condition that after a new discovery the preference ranking should remain unchanged over acts to which the discovery is irrelevant. Together with other natural axioms, it characterizes a model in which the decision maker's belief evolves over time in order that the marginal distribution of a new belief induced over the old state space coincides with the old belief. It is extended in order to encompass both discovery and learning events, and we characterize the model with an additional property that the decision maker's belief updating follows Bayes' rule when she learns events.