In the paper, infinite horizon differential games on networks are considered. The cooperative version of the game is proposed, and the special type of characteristic function is introduced. It is proved that the constructed cooperative game is convex. Using the properties of payoff functions and the constructed characteristic function, the Shapley Value is computed. It is also proved that in this special class of differential games the Shapley value is time-consistent. In non cooperative case as solution concept the Nash Equilibrium is considered. Moreover, a special subclass of Nash equilibrium, based on threat and punishment strategies, is derived. Additionally, we compute the Price of Stability (PoS).