We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over the coalitional behavior of the outsiders, i.e., it assigns various probability distributions over the set of partitions that the outsiders can form. These beliefs are not necessarily consistent with respect to the actual choices of the outsiders. We apply this framework to symmetric partition function form games characterized by either positive or negative externalities and we derive conditions on coalitional beliefs that guarantee the non-emptiness of the core of the induced games.

翻译：我们重新审视了分区函数形式的博弈，即联盟的收益依赖于整个参与者集合划分的合作博弈。我们假设每个联盟在计算自身价值时，持有关于外部参与者联盟行为的概率信念，即对外部参与者可能形成的各种分区赋予一定的概率分布。这些信念不一定与外部参与者的实际选择保持一致。我们将该框架应用于具有正外部性或负外部性特征的对称分区函数形式博弈，并推导出保证诱导博弈核心非空的联盟信念条件。