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

This article analyzes how interdependencies in financial networks can cause self-fulfilling insolvencies and multiple equilibrium outcomes, focusing on networks of banks linked by unsecured debt contracts. It establishes that multiple equilibria arise if and only if certain dependency cycles exist in the network, with the best equilibrium minimizing defaults and the worst maximizing them. The paper characterizes systemic solvency conditions for both best and worst equilibria and shows that finding the minimum-cost bailout policy to prevent self-fulfilling defaults in nonbest equilibria is strongly NP-hard due to the complexity of overlapping cycles and the order of bailouts. However, it provides intuitive insights and algorithms leveraging indirect bailout benefits, proving that systemic solvency can be ensured at a cost never exceeding half the total shortfall, and identifies simpler optimal bailout strategies in specific network structures such as disjoint cycles and core-periphery (star) networks, where bailing out peripheral banks first is often optimal. The study also discusses implications for crisis management, including the benefits of payment netting, portfolio compression, and central counterparties in reducing systemic fragility.