Partition function form games with probabilistic beliefs

TL;DR

This paper explores cooperative partition function games where coalitions hold probabilistic beliefs about outsiders' behaviors, analyzing conditions for core stability under externalities.

Contribution

It introduces a framework for probabilistic beliefs in partition function games and derives core non-emptiness conditions for symmetric externality cases.

Findings

Conditions for core non-emptiness under probabilistic beliefs.

Application to symmetric games with positive or negative externalities.

Framework accommodates inconsistent beliefs about outsiders' behavior.

Abstract

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.