This paper presents a time-consistent dynamic Shapley value imputation for a class of differential network games. A novel form for measuring the worth of coalitions - named as cooperative-trajectory characteristic function - is developed for the Shapley value imputation. This new class of characteristic functions is evaluated along the cooperative trajectory. It measures the worth of coalitions under the process of cooperation instead of under minmax confrontation or the Nash non-cooperative stance. The resultant dynamic Shapley value imputation yields a new cooperative solution in differential network games.