Informal Insurance in Social Networks

This paper studies informal insurance across networks of individuals. Two characteristics are fundamental to the model developed here: First, informal insurance is a bilateral activity, and rarely involves explicit arrangements across several people. Second, insurance is a social activity, and transfers are often based on norms. In the model studied here, only directly linked agents make transfers to each other, although they are aware of the (aggregate) transfers each makes to third parties. An insurance scheme for the network as a whole is an equilibrium of several interacting bilateral arrangements. This model serves as a starting point for investigating stable insurance networks, in which all agents actually have private incentives to abide by the ongoing insurance arrangement. The resulting analysis shows that network links have two distinct and possibly conflicting roles to play. First, they act as conduits for transfers, and in this way this make better insurance possible. Second, they act as conduits for information, and in this sense they affect the severity of punishments for noncompliance with the scheme. A principal task of this paper is to describe how these two forces interact, and in the process characterize stable networks. The concept of "sparse" networks, in which the removal of certain links increases the number of network components, is crucial in this characterization. As corollaries, we found that both "thickly connected" networks(such as the complete graph) and "thinly connected" networks (such as trees) are likely to be stable, whereas intermediate degrees of connectedness jeopardize stability. Finally, we study in more detail the notion of networks as conduits for transfers, by simply assuming a punishment structure (such as autarky) that is independent of the precise architecture of the tree. This allows us to isolate a bottleneck effect: the presence of certain key agents who act as bridges for several transfers. Bottlenecks are captured well in a feature of trees that we call decomposability, and we show that all decomposable networks have the same stability properties and that these are the least likely to be stable.