Network differential games with partner sets are considered. The payoff of each player depends on his actions and the actions of the players from his partner set. The article proposes a cooperative version of the game. A special-type characteristic function that takes into account players in partner sets is introduced, and its superadditivity is proved. As a solution, we propose a C-core, for which nonemptiness is proved, as well as a Shapley value and a $$\tau $$-value.