Abstract
We note that in environments such as exploration problems, in which agents have to choose a single action out of several in each period, an agent's preferences over different strategies can only reveal the margins of her beliefs. However, classical notions of Bayesian updating regard the joint distribution. We develop the relevant environment and tools to solve this issue: We introduce a necessary and sufficient condition on the margins of an agent's beliefs to be consistent with an exchangeable process. Such a consistent process is typically not unique; contemporaneous correlation cannot be identified. We conclude that contemporaneous correlations do not affect the optimal strategy in classical bandit problems.
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