Endogenous formation of multiple social groups

Abstract

AbstractThis paper explores a model of group membership formation in which agents decide to join or not multiple social groups. The membership formation process induces a bipartite graph structure with social groups listed on one side and agents listed on the other side. Among members of multiple social groups, we consider two decisive types of agents: the grand star and the mini star. The former type is the unique agent in a society who participates in all social groups. The latter type includes agents who participate in more than one, but not all, social groups such that every social group pair has one and only one common member. We analyze the efficiency and stability conditions of group membership formation, and we establish sufficient conditions under which a connected graph that contains either a grand star or a set of mini stars becomes the unique strongly efficient and stable graph.