A class of differential games on networks is considered. 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. It is assumed that interaction on the network is possible between neighboring players and between players connected by paths whose length does not exceed a given value. It is shown that in such games the characteristic function is convex even if there are cycles in the network. The core is used as cooperative optimality principles. A necessary and sufficient condition for an imputation to belong to the core is obtained. The network differential resource extraction game is investigated as an example.