We analyze how interdependencies between organizations in financial networks can lead to multiple possible equilibrium outcomes. A multiplicity arises if and only if there exists a certain type of dependency cycle in the network that allows for self-fulfilling chains of defaults. We provide necessary and sufficient conditions for banks' solvency in any equilibrium. Building on these conditions, we characterize the minimum bailout payments needed to ensure systemic solvency, as well as how solvency can be ensured by guaranteeing a specific set of debt payments. Bailout injections needed to eliminate self-fulfilling cycles of defaults (credit freezes) are fully recoverable, while those needed to prevent cascading defaults outside of cycles are not. We show that the minimum bailout problem is computationally hard, but provide an upper bound on optimal payments and show that the problem has intuitive solutions in specific network structures such as those with disjoint cycles or a core-periphery structure.

翻译：我们分析了金融网络中组织间的相互依存关系如何导致多种可能的均衡结果。当且仅当网络中存在的某种依赖循环允许自我实现的违约链时，多重性才会出现。我们给出了任意均衡下银行偿付能力的必要充分条件。基于这些条件，我们刻画了确保系统偿付能力所需的最低救助支付额，以及如何通过担保特定债务支付来确保偿付能力。消除自我实现违约循环（信用冻结）所需的救助注资可完全回收，而防止循环外连锁违约所需的救助则无法回收。我们证明最小救助问题具有计算复杂性，但给出了最优支付的上界，并表明该问题在特定网络结构（如无环循环或核心-外围结构）中具有直观解。