In the presented paper, we consider dynamic network games with partner sets in which players cooperate to get the best outcomes. Using the game structure the two-level cooperative scheme is introduced. On the first level, the partner sets are considered as players, and the cooperative behavior is used in the game with partner sets, it is assumed that partners intend to maximize their joint payoff and then distribute it using a given optimality principle as usual in cooperative game theory. On the second level, the gain obtained by each player (partner set) is distributed among members of this partner set. The distribution of this gain is also made based on solution concepts from classical cooperative game theory. Since the game is dynamic the problem of time-consistency (dynamic stability) of the proposed two-level solution arises. To simplify the calculations the new characteristic function is introduced based on the possibility of cutting connections by players outside the coalition. Also, this newly defined characteristic function allows construction of time-consistent (dynamically stable) solutions.