Coalition Structure Generation For Partition Function Games Utilizing A Concise Graphical Representation

Coalition Structure Generation (CSG), a main research issue in the domain of coalition games, involves partitioning agents into exhaustive and disjoint coalitions to optimize the social welfare. The advent of compact representation schemes, such as Partition Decision Trees (PDTs), promotes the efficiency of solving CSG problems.This paper studies the CSG problem for partition function games (PFGs) which are coalitional games with externalities. In PFGs, each value of a coalition depends on how the other agents are partitioned. We apply PDTs to represent PFGs and present two methods to solve CSG problems: a depth-first branch-and-bound algorithm and MaxSAT encoding.