We built a time-consistent cooperative solution for the class of dynamic games played over event trees in the context where the structure of the tree is given, but the players have different beliefs about the transition probabilities between nodes. Our three-step approach is as follows. First, we consider three alternative methods for aggregating the players probability distributions, and assume that the players agree to adopt one of them if they decide to cooperate. Second, we determine the Nash bargaining outcomes for the whole duration of the game. Finally, to insure sustainability of cooperation throughout the whole duration of the game, we propose two time-consistent decompositions over nodes of each player's cooperative share, namely, a proportion-consistent and a node-consistent allocation. We illustrate our results with a simple Cournot oligopoly with capacity constraints.