Fair allocation in hierarchies: A compromise between marginalism and egalitarianism

This paper explores the fair allocation of economic surplus among individuals within hierarchical social structures, incorporating the seemingly conflicting principles of marginalism and egalitarianism. We formalize this situation as cooperative games with permission structures and introduce a novel class of allocation rules called egalitarian permission values, extending the traditional egalitarian Shapley values. Our main contribution lies in establishing an axiomatic foundation for this class of rules through a monotonicity axiom. Additionally, we provide a monotonicity-based foundation for the permission value as a special case. Our results also reveal that, in the presence of hierarchical structures, a monotonicity property alone is insufficient to justify the adoption of linear allocation rules, contrasting with the conventional findings in the literature.