We develop a simple model that looks at the incentives of private banks to behave prudentially and undertake costly efforts to lower the probability of bankruptcy or having to be bailed out by a lender of last resort. Government regulators can force banks to increase efforts beyond the privately optimal level. We contrast the national case under autarky with the case of an integrated banking market with bank cross-holdings. Because banks will exert a greater overall effort to monitor their foreign activities, financial integration might lead to more rather than less prudential behavior. Neither needs financial integration lead to a regulatory race to the bottom. We use the framework to investigate the impact of regulatory coordination on bank efforts and discuss incentives for banks to organize their foreign holdings in the form or branches or subsidiaries. We show that the absence of a common lender of last resort can reduce the probability of a financial crisis.