Hierarchical organization structures and constraints on coalition formation

This paper studies the constraints in coalition formation that result from a hierarchical organization structure on the class of players in a cooperative game with transferable utilities. If one assumes that the superiors of a certain individual have to give permission to the actions undertaken by the individual, ten one arrives at a limited collection of formable or autonomous coalitions. This resulting collection is a lattice of subsets on the player set. The authors show that if the collection of formable coalition is limited to a lattice, the core allows for (infinite) exploitation of subordinates. For discerning lattices they are able to generalize the results of Weber, namely the core is a subset of the convex hull of the collection of all attainable marginal contribution vectors plys a fixed cone. This relation is an equality if and only if the game is convex. This extends the results of Shapley and Ichiishi.