Risk-sharing agreements on social networks

This paper investigates self-enforcing risk-sharing agreements in a society, if only binary transfers are allowed, among agents connected by social links. A social link between two agents represents another activity they are involved in together. It also serves as a collateral, to enforce transfer payments specified by the risk-sharing agreement. Given an arbitrary network structure and link values, we characterize the set of incentive compatible agreements, and its efficient frontier. All efficient agreements imply that for any endowment vector realization there are connected blocks of players who completely coinsure each other, and links that connect the block to outsiders operate at full capacity. However, these blocks are different for different endowment realizations, as opposed to models which specify constant risk-sharing groups. We show that under general conditions (i) full risk-sharing is not possible in large networks; (ii) the covariance of the consumption of two distant agents is small; (iii) changing only the correlation of individual endowments does not change the set of efficient risk-sharing agreements, only ex ante welfare. We relate our results to empirical findings on social insurance within and across villages in developing countries.