Robust Merging of Information

When multiple sources of information are available, any decision must take into account their correlation. If information about this correlation is lacking, an agent may find it desirable to make a decision that is robust to possible correlations. Our main results characterize the strategies that are robust to possible hidden correlations. In particular, with two states and two actions, the robustly optimal strategy pays attention to a single information source, ignoring all others. More generally, the robustly optimal strategy may need to combine multiple information sources, but can be constructed quite simply by using a decomposition of the original problem into separate decision problems, each requiring attention to only one information source. An implication is that an information source generates value to the agent if and only if it is best for at least one of these decomposed problems.