Group formation in risk-sharing arrangements

We study informal insurance within communities, explicitly recognizing the possibility that subgroups of individuals may destabilize insurance arrangements among the larger group. We therefore consider self-enforcing risk-sharing agreements that are robust not only to single-person deviations but also to potential deviations by subgroups. However, such deviations must be credible, in the sense that the subgroup must pass exactly the same test that we apply to the entire group; it must itself employ some self-enforcing risk-sharing agreement. We observe that the stability of subgroups is inimical to the stability of the group as a whole. Two surprising consequences of this analysis are that stable groups have (uniformly) bounded size, a result in sharp contrast to the individual-deviation problem, and that the degree of risk-sharing in a community is generally non-monotonic in the level of uncertainty or need for insurance in the community.