When agents have different needs for a public facility but serving a given agent allows serving all agents with smaller needs than his without any extra cost, how should the agents divide the cost of the facility among themselves? We provide a strategic implementation of the Shapley value for this class of cost‐sharing problems. We introduce a three‐stage extensive form game that respects individual rationality and show that there is one and only one subgame‐perfect equilibrium outcome of the game. Moreover, it is the allocation assigned by the Shapley value.