Risk-sharing and contagion in networks

We investigate the trade-off, arising in financial networks, between higher risksharing and greater exposure to contagion when the connectivity increases. We find that with shock distributions displaying "fat" tails, extreme segmentation into small components is optimal, while minimal segmentation and high density of connections are optimal with distributions exhibiting "thin" tails. For less regular distributions, intermediate degrees of segmentation and sparser connections are optimal. If firms are heterogeneous, optimality requires perfect assortativity in their linkages. In general, however, a conflict arises between optimality and individual incentives to establish linkages, due to a "size externality" not internalized by firms.