In the talk, we examine the class of differential games on networks. The construction of cooperative optimality principles using a special type of characteristic function that takes into account the network structure of the game is investigated. Various conditions of possible interaction of players are assumed. It is shown that in such games the characteristic function is convex. The core is used as a cooperative optimality principle. A necessary and sufficient condition for an imputation to belong to the core is obtained. Strong time consistency of the core is proved.