Hierarchical organization structures and constraints on coalition formation

J. Derks, R. Gilles

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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).
Original languageEnglish
Pages (from-to)147-163
Number of pages17
JournalInternational Journal of Game Theory
Volume24
Issue number2
DOIs
Publication statusPublished - 1995

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