Informal Insurance in Social Networks

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Abstract
This paper studies bilateral insurance schemes across networks of individuals. While transfers are based on social norms, each individual must have the incentive to abide by those norms, and so we investigate the structure of stable insurance networks, in which self-enforcement constraints are satisfied. Network links play two distinct and possibly conflictual roles. First, they act as conduits for transfers. Second, they act as conduits for information. These features affect the scope for insurance, as well as the severity of punishments in the event of noncompliance. Their interaction leads to a characterization of stable networks as networks which are suitably sparse, the degree of sparseness being related to the length of the minimal cycle that connects any triple of agents. As corollaries, we find 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 network. 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.

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