Hierarchical Organization Structures and Constraints on Coalition Formation

Jean Derks and Robert P Gilles

International Journal of Game Theory, 1995, vol. 24, issue 2, 147-63

Abstract: 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, then one arrives at a limited collection of formable or autonomous coalitions. This resulting collection is a lattice of subsets on the player set. We show that if the collection of formable coalitions is limited to a lattice, the core allows for (infinite) exploitation of subordinates. For discerning lattices we are able to generalize the results of Weber (1988), namely the core is a subset of the convex hull of the collection of all attainable marginal contribution vectors plus a fixed cone. This relation is an equality if and only if the game is convex. This extends the results of Shapley (1971) and Ichiishi (1981).

Date: 1995
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