PGN-Value for Dynamic Games with Changing Partial Cooperation

The game with partial cooperation with perfect information in extensive form is considered. The optimal solution PMS-vector in such a game has been proposed in [Petrosjan, 2000].
In our paper the characteristic functions are defined for each coalition $S$ $(S\subset N)$ according to some unified principle (for example, the best response to Nash equilibrium), but they are not necessarily supper additive.
A new principle of optimal behavior in such a game is established, based on the nucleolus as optimality principle for the allocation of coalitional payoff. On the first part of this paper, we have made an assumption that once the player announced that he would take cooperative behavior and never change this announcement, namely, he could not leave the coalition.
Based on this assumption, we construct algorithm for the solution of the game. And in the second part in this paper, we try to eliminate this limitation and, so, we construct a new method to achieve the goal. Algorithm of $PGN$-value of this kind of a game is offered and the optimal trajectory is found. The existence and uniqueness of nucleolus leads to the existence and uniqueness of the new solution.