I develop a model of financial networks in which linkages not only spread contagion, but also induce private sector bailouts, where liquid banks bail out illiquid banks because of the threat of contagion. Introducing this bailout possibility, I show that linkages may be optimal ex ante because they allow banks to obtain some mutual insurance even though formal commitments are impossible. However, in some cases (e.g., when liquidity is concentrated among a small group of banks), the whole network may collapse. I also characterize the optimal network size and apply the results to joint liability arrangements and payment systems.

Should regulators reveal the models they use to stress‐test banks? In our setting, revealing leads to gaming, but secrecy can induce banks to underinvest in socially desirable assets for fear of failing the test. We show that although the regulator can solve this underinvestment problem by making the test easier, some disclosure may still be optimal (e.g., if banks have high appetite for risk or if capital shortfalls are not very costly). Cutoff rules are optimal within monotone disclosure rules, but more generally optimal disclosure is single‐peaked. We discuss policy implications and offer applications beyond stress tests.