Partition function form games with probabilistic beliefs

2026-05-02

AI Summary

This study addresses the challenge of cooperative stability in partition function form games, where coalition payoffs depend on the entire partition structure and coalitions hold heterogeneous probabilistic beliefs about the behavior of external players. Departing from the conventional assumption of common expectations, the paper introduces a belief mechanism grounded in probability distributions. By modeling each coalition’s uncertainty regarding external partitions as a probabilistic belief and integrating this with the partition function game framework and core analysis, the authors derive sufficient conditions that guarantee a non-empty core in the induced game. This work extends the stability theory for symmetric externality-embedded games to environments characterized by uncertainty, offering a novel existence guarantee for cooperative equilibria in more realistic strategic settings.

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.

Problem

• partition function form games
• probabilistic beliefs
• core non-emptiness
• externalities
• coalitional behavior

Innovation

• partition function form games
• probabilistic beliefs
• coalitional behavior
• core non-emptiness
• externalities