Credit Freezes, Equilibrium Multiplicity, and Optimal Bailouts in Financial Networks

We analyze how interdependencies in financial networks can lead to self-fulfilling insolvencies and multiple possible equilibrium outcomes. We show that multiplicity arises if and only if there exists a certain type of dependency cycle in the network, and characterize banks' solvency in any equilibrium. We use this analysis to understand how to inject capital into banks so as to ensure solvency of all at minimum cost. We show that finding the cheapest bailout policy that prevents self-fulfilling insolvencies is computationally hard (and hard to approximate), but that the problem has intuitive solutions in specific network structures. Bailouts have an indirect value as making a bank solvent improves its creditors' balance-sheets and reduces their bailout costs, and we show how a simple algorithm that leverages these indirect benefits ensures systemic solvency at a total cost that never exceeds half of the total overall shortfall. In core-periphery networks, indirect bailouts -- whereby the regulator bails out peripheral banks first as opposed to targeting core banks directly -- are part of an optimal policy