An instrumental approach to the value of information

We consider an agent who acquires information on a state of nature from an information structure before facing a decision problem. How much information is worth depends jointly on the decision problem and on the information structure. We represent the decision problem by the set of possible payoffs indexed by states of nature. We establish and exploit the duality between this set on one hand and the value of information function, which maps beliefs to expected payoffs under optimal actions at these beliefs, on the other. We then derive global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only.

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