Stable organizations with externalities

We study the stability properties of organizations in partition function games, describing cooperative situations with externalities. An organization is defined as a group of agents, together with a set of bilateral relations, formally, a connected graph. Because of the presence of externalities, the profitability of coalitional threats to an organization depend on the reaction of non coalitional members. This reaction is likely to depend on the links that non coalitional members maintain in the organization. We show that this directly implies that minimally connected organizations emerge under positive externalities, while the fully connected organization emerges under negative. This result is shown to hold independently of the adopted payoff imputation rule. Sharper predictions are possible for the specific case of the egalitarian rule. Here, if only coalitions that are connected in the organization can effectively object to it, the star organization prevails under positive externalities, and the wheel, a non fully connected organization, prevails under negative.