Optimal Fragile Financial Networks

We study a financial network characterized by depositors, banks and their shareholders. Belonging to a financial network is beneficial for both the depositors and banks' shareholders since the return to investment increases with the number of banks connected. However, the network is fragile since banks, which invest on behalf of the depositors, have an incentive to gamble with depositors' money when not sufficiently capitalized. The bankruptcy of a bank negatively affects the banks connected to it in the network. First, we compute the social planner solution and the efficient financial network is characterized by a core-periphery structure. Second, we analyze the decentralized solution showing that participating in a fragile financial network is ex-ante optimal when the probability of bankruptcy is sufficiently low, giving rationale of financial fragility as a rare phenomenon. Finally, we analyze the efficiency of the decentralized financial network. On the one hand, if the probability of bankruptcy is sufficiently low the structure of the decentralized financial network coincides with the efficient one. However, in the decentralized network some banks will gamble as compared to the socially preferred outcome. On the other hand, when the probability of bankruptcy is sufficiently high, the decentralized network does not necessarily coincide with the optimal one, and inefficiencies may arise