Group Stability of Hierarchies in Games with Spillovers

In a recent paper, Demange (2004) has shown that hierarchical organizations can guarantee the existence of stable cooperative outcomes by appropriately allocating the blocking power to a subset of coalitions, the “teams”. This paper extends the analysis of Demange to cooperative problems with spillovers. We show that if blocking coalitions have “pessimistic expectations” on the reaction of outsiders, in all cooperative problems there exists an allocation which is blocked by no team. We also study the case of ”passive expectations”, for which the same result holds in all games with negative spillovers, while stable allocations may fail to exist in games with positive spillovers. In the latter class of games, however, hierarchies are shown to be the most stable organizational forms.