This paper studies the formation of the grand coalition of a cooperative game by investigating its possible internal dynamics. Each coalition is capable of forcing all players to reconsider the current state of the game when it does not provide sufficient payoff. Different coalitions may ask for contradictory evolutions, leading to the impossibility of the grand coalition forming. In this paper, we give a characterization of the impossibility, for a given state, of finding a new state dominating the previous one such that each aggrieved coalition has a satisfactory payoff. To do so, we develop new polyhedral tools related to a new family of polyhedra, appearing in numerous situations in cooperative game theory.