Governments typically respond to a run on the banking system by temporarily freezing deposits and by rescheduling payments to depositors. Depositors may even be required to demonstrate an urgent need for funds before being allowed to withdraw. We study ex post efficient policy responses to a bank run and the ex ante incentives these responses create. Given that a run is underway, the efficient response is typically not to freeze all remaining deposits, since this would impose heavy costs on individuals with urgent withdrawal needs. Instead, (benevolent) government institutions would allow additional withdrawals, creating further strain on the banking system. We show that when depositors anticipate these extra withdrawals, their incentives to participate in the run actually increase. In fact, ex post efficient interventions can generate the conditions necessary for a self-fulfilling run to occur.