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：本文通过研究合作博弈的内部动态机制，探讨大联盟的形成过程。当现有博弈状态无法提供足够收益时，任何联盟均有权要求全体参与者重新评估当前状态。不同联盟可能提出相互矛盾的演化要求，从而导致大联盟无法形成。本文针对给定博弈状态，刻画了无法找到满足以下条件的新状态之特征：新状态需优于原状态，且能使每个利益受损联盟获得满意收益。为此，我们发展了与新型多面体族相关的新多面体分析工具，这类多面体在合作博弈论的诸多情境中频繁出现。