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

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