Quoting Jack Hirshleifer, ``Information is of value only if it can affect action". We consider an economic agent who acquires information on a state of nature before facing a decision problem. By using a duality between actions/payoffs and beliefs, we shed light on the value of information and show how it can be measured by the impact of information on optimal actions. More precisely, using tools from convex analysis, we relate
the geometry of the actions/payoffs set --- kink, flat, curved --- to the economic agent behaviour --- undecided, confident, flexible. We apply our results to analyze the impact of a small amount of information (marginal value of information at the null).