The value of information: The case of signal-dependent opportunity sets

We generalize the economic decision problem considered by Blackwell (1953) in which a decision-maker chooses an action after observing a signal correlated to the state of nature. Unlike Blackwell's case where the feasible set is fixed, in our framework the feasible set of actions depends on the signal and the information system. We argue that such a framework has more significance to economic models. As was demonstrated by Hirshleifer (1971) in such cases, contrary to Blackwell's well-known result, more information may be disadvantageous. We derive conditions for this general model which guarantee that more information is beneficial.