The problem in which some agents joint together to realize a set of projects and must decide how to share its cost may be seen as a cooperative cost game. In many instances, total cost may naturally be decomposed into joint costs and costs that are specific to individual agents. We show that the maximal amount that can be attributed directly to each agent while yielding a problem for the joint cost that remains a cost game, is given by the minimal incremental cost of adding this agent to any of the possible coalitions of other agents. Thus, for concave games, it is given by the incremental cost of adding the agent to all others. We also show that a concave game yields a reduced game that is itself concave.