Solutions of cooperative differential games with partner sets

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 and introduces a special type of characteristic function that takes into account players in partner sets and proves its superadditivity. As a solution, we propose a $C$-core which non-emptiness is proved, as well as a Shapley value and a $\tau$-value.