Coalition formation under power relations

We analyze the structure of a society driven by power relations. Our model has an exogenous power relation over the set of coalitions of agents. Agents determine the social order by forming coalitions. The power relations determine the ranking of agents in society for any social order. We study a cooperative game in partition function form and introduce a solution concept, the stable social order, which exists and includes the core. We investigate a refinement, the strongly stable social order, which incorporates a notion of robustness to variable power relations. We provide a complete characterization of strongly stable social orders.