MaxSAT encoding for MC-net-based coalition structure generation problem with externalities

Coalition Structure Generation (CSG) is a main research issue in the domain of coalition games. A majority of existing works assume that the value of a coalition is independent of others in the coalition structure. Recently, there has been interest in a more realistic settings, where the value of a coalition is affected by the formation of other coalitions. This effect is known as externality. The focus of this paper is to make use of Maximum Satisfiability (MaxSAT) to solve the CSG problem where externalities may exist. In order to reduce the exponentially growing number of possible solutions in the CSG problem, we follow the previous works by representing the CSG problem as sets of rules in MC-nets (without externalities) and embedded MC-nets (with externalities). Specifically, enlightened by the previous MC-net-based algorithms exploiting the constraints among rule relations to solve the CSG problem, we encode such constraints into weighted partial MaxSAT (WPM) formulas. Experimental results demonstrate that an off-the-shelf MaxSAT solver achieves significant improvements compared to the previous algorithm for the same set of problem instances.