Group Stability of Hierarchies in Games with Spillovers

This paper studies the stability properties of hierarchies in cooperative problems with spillovers. The analysis builds on a recent paper by Demange [Demange, G. (2004) “On Group Stability in Hierarchies and Networks”, Journal of Political Economy 112(4), 754–778.], in which hierarchical structures are shown to attain stability by limiting the ability of certain coalitions to act autonomously and object to cooperative outcomes. We show that the stability properties of hierarchies crucially depend on the interplay of spillovers with the expectations that blocking coalitions form on the reaction of outsiders. In particular, we focus on pessimistic, passive and optimistic expectations, and on the classes of negative and positive spillovers. Under negative spillovers, hierarchies are shown to guarantee stability in all cooperative problems, but fail to sustain as stable all cooperative outcomes that are instead stable within non hierarchical organizations. Under positive spillovers we obtain opposite results: hierarchies fail to always guarantee stability, but sustain as stable all cooperative outcomes that are stable in non hierarchical organizations.