We model a banking union of two countries whose banking sectors di↵er in their average probability of failure and externalities between the two countries arise from cross-border bank ownership. The two countries face (i) a regulatory (supervisory) decision of which banks are to be shut down before they can go bankrupt, and (ii) a bailout decision of who pays for banks that have failed despite regulatory oversight. Each of these choices can either be taken in a centralized or in a decentralized way. In our benchmark model the two countries always agree on a centralized regulation policy. In contrast, bailout policies are centralized only when international spillovers from cross-border bank ownership are strong, and banking sectors are highly profitable