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 orautonomous 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).
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We would like to thank Rene van den Brink, Hans Haller, Nancy Lutz, Bruno Parigi, and an anonymous referee for their remarks on a previous draft of this paper and Alan Kirman for his questions that raised the issue as discussed in this paper.
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Derks, J.J.M., Giles, R.P. Hierarchical organization structures and constraints on coalition formation. Int J Game Theory 24, 147–163 (1995). https://doi.org/10.1007/BF01240039
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DOI: https://doi.org/10.1007/BF01240039