Structural stability of coalitions: A formal model highlighting the role of participants positioned between members and neutral actors

Given a fixed network that links various actors, we introduce a formal model that describes the structural stability of coalitions. To this end, we used the partition of the set of all actors in three distinct positions: members, i.e., those who are central to a coalition; participants, i.e., those who are not actively engaged with the issues at hand; neutral actors, i.e., non-members, those who are not party to any interests and outside the coalition. Using the language of networks, we formulated three assumptions that may be used to characterize the stability of this partition. We paid particular attention to the role of participants as they facilitate or complicate extensions of a given coalition. Given the fixed network, we (1) illustrate the verification of the stability of a coalition, (2) provide existence results of stable coalitions, and (3) set the limits to their credible extensions. Our three formal assumptions may serve as a platform for discussions regarding the stability of coalitions.