Qualitative Coalitional Reasoning with Preferences

Qualitative coalitional games (QCGs) are a variation of conventional coalitional games in which each coalition may choose to cooperate in a number of different ways, with different choices resulting in potentially different sets of goals being achieved; each agent is associated with a set of goals, the intuition being that an agent is “satisfied” if any of its goals are achieved, but is indifferent between them. In this paper, we extend the framework of QCGs to incorporate preferences that agents have over their goals. In addition to establishing some basic properties of QCGs with Preferences (QCGPs), we investigate and characterise the complexity of six natural decision problems associated with QCGPs. For example, we prove that the problem of establishing Pareto optimality of a goal set with respect to some coalition is co-NP-complete. We end with some brief conclusions and a discussion of related work.