Constitutions and groups

We develop a general theoretical framework that allows us to study the group structures that are going to emerge at equilibrium in overlapping coalition settings. We introduce the notion of constitution in order to model for each group the rules governing both the composition of the group and the conditions needed to leave the group and/or to become a new member of the group. We propose the concept of constitutional stability to study the group structures that are going to emerge at equilibrium. This concept generalizes previous stability concepts in the literature in which the constitutional rules were exogenously given or not explicitly considered. We combine requirements on constitutions and preferences for guaranteeing both the existence and the emergence of constitutionally stable group structures. Finally, we show how these results are useful to identify constitutionally stable group structures in many-to-many matchings.