On the Stability of Hierarchies in Games with Externalities

We study the group stability of collective decision making when society is organized according to a non directed graph, and groups' payoff possibilities are given by a partition function. We focus on the stability properties of hierarchical organizations, formally described by minimally connected graphs (or trees). Building on previous works by Greenberg and Weber (1986, 1993) and by Demange (1994, 2001), we restrict the ability of raising objections to proposed payoff imputations to coalitions that are connected in the organization. We show that the stability properties of hierachical organizations, proved in Demange (1994, 2002), extend to partition function games with negative externalities. Under positive externalities, although not ensuring social stability, hierarchies are the "most stable" organizational forms for society.