This article investigates stable and efficient networks in the context of risk sharing, when it is costly to establish and maintain relationships that facilitate risk sharing. We find a novel trade-off between efficiency and equality: the most stable efficient networks also generate the most inequality. We then suppose that individuals can be split into groups, assuming that incomes across groups are less correlated than within a group but relationships across groups are more costly to form. The tension between efficiency and equality extends to these correlated income structures. More-central agents have stronger incentives to form across-group links, reaffirming the efficiency benefits of having highly central agents. Our results are robust to many extensions. In general, endogenously formed networks in the risk-sharing context tend to exhibit highly asymmetric structures, which can lead to stark inequalities in consumption levels.

This article considers the effect of contracting limitations in risk-sharing networks, arising for example from observability, verifiability, complexity, or cultural constraints. We derive necessary and sufficient conditions for Pareto efficiency under these constraints in a general setting, and we provide an explicit characterization of Pareto efficient bilateral transfer profiles under CARA utility and normally distributed endowments. Our model predicts that network centrality is positively correlated with consumption volatility, as more central agents become quasi-insurance providers to more peripheral agents. The proposed framework has important implications for the empirical specification of risk-sharing tests, allowing for local risk-sharing groups that overlap within the village network.