Handling Negative Value Rules in MC-net-based Coalition Structure Generation

A Coalition Structure Generation (CSG) problem involves partitioning a set of agents into coalitions so that the social surplus is maximized. Recently, Ohta et al. developed an efficient algorithm for solving CSG assuming that a characteristic function is represented by a set of rules, such as marginal contribution networks (MC-nets). In this paper, we extend the formalization of CSG in Ohta et al. so that it can handle negative value rules. Here, we assume that a characteristic function is represented by either MC-nets (without externalities) or embedded MC-nets (with externalities). Allowing negative value rules is important since it can reduce the efforts for describing a characteristic function. In particular, in many realistic situations, it is natural to assume that a coalition has negative externalitie