Internal Hierarchy and Stable Coalition Structures

In deciding whether to join a coalition or not, an agent must consider both i) the expected power of the coalition and ii) her position in the vertical structure within the coalition. We establish the existence of a positive relationship between the degree of inequality in remuneration across ranks within coalitions and the number of coalitions to be formed endogenously in stable systems. An inherent feature of such coalitions is that they are mixed and balanced, rather than segregated, in terms of members abilities. When the surplus of a coalition is assumed to be linear in its relative power conditional on its size, we also establish the existence of stable systems and characterise them fully: a system is stable if and only if all coalitions are of an ecient size and every agent is paid her marginal contribution.