On the computational complexity of coalitional resource games

We study Coalitional Resource Games (CRGs), a variation of Qualitative Coalitional Games (QCGs) in which each agent is endowed with a set of resources, and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources. We investigate and classify the computational complexity of a number of natural decision problems for CRGs, over and above those previously investigated for QCGs in general. For example, we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound (i.e., a limit value for every resource) is co-NP-complete. We then investigate the relationship between CRGs and QCGs, and in particular the extent to which it is possible to translate between the two models. We first characterise the complexity of determining equivalence between CRGs and QCGs. We then show that it is always possible to translate any given CRG into a succinct equivalent QCG, and that it is not always possible to translate a QCG into an equivalent CRG; we establish some necessary and some sufficient conditions for a translation from QCGs to CRGs to be possible, and show that even where an equivalent CRG exists, it may have size exponential in the number of goals and agents of its source QCG. © 2006 Elsevier B.V. All rights reserved.