Partition Function Form Games With Probabilistic Beliefs

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. We apply this framework to symmetric games with either positive or negative externalities and we derive conditions on coalitional beliefs that guarantee the non-emptiness of the core.