Coalition Structure Generation and CS-core: Results on the Tractability Frontier for games represented by MC-nets

The coalition structure generation (CSG) problem consists in partitioning a group of agents into coalitions to maximize the sum of their values. We consider here the case of coalitional games whose characteristic function is compactly represented by a set of weighted conjunctive formulae (an MC-net). In this context the CSG problem is known to be computationally hard in general. In this paper, we first study some key parameters of MCnets that complicate solving make the CSG problem. Then we consider a specific class of MC-nets, called bipolar MCnets, and prove that the CSG problem is polynomial for this class. Finally, we show that the CS-core of a game represented by a bipolar MC-net is never empty, and that an imputation belonging to the CS-core can be computed in polynomial time.