Our concern is the extension of the theory of the Shapley value to problems involving externalities. Using the standard axiom systems behind the Shapley value leads to the identification of bounds on players' payoffs around an “externality‐free” value. The approach determines the direction and maximum size of Pigouvian‐like transfers among players, transfers based on the specific nature of externalities that are compatible with basic normative principles. Examples are provided to illustrate the approach and to draw comparisons with previous literature.