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.

翻译：本文通过考察合作博弈可能的内在动态过程，研究大联盟的形成机制。当现有博弈状态无法提供足够收益时，任一联盟均能迫使所有参与者重新评估当前状态。不同联盟可能要求相互矛盾的演化路径，从而导致大联盟无法形成。本文针对给定博弈状态，刻画了无法找到支配原状态且使每个受损联盟均获得满意收益的新状态的特征条件。为此，我们发展了与一类新型多面体相关的多面体分析工具，这类多面体在合作博弈论的诸多情境中广泛存在。