In the presence of economies of scale, depositors' expectations are shown to give rise to vertical differentiation and to yield multiple market equilibria, some of which exhibit institutional or systemic collapse. This fragility is due to a coordination problem among depositors and not to bank competition. Nevertheless, failure perceptions do influence rivalry which in turn affects the failure probability in particular equilibria. Deposit insurance improves welfare by preventing collapse, extending the market, and minimizing frictions. However, deposit insurance also may induce fiercer competition for deposits and increase the deadweight losses associated with failing institutions. The welfare impact of deposit insurance is shown to depend on market structure, and is thus ambiguous even in a world of full liability and no moral hazard in bank investments.Journal of Economic LiteratureClassification Numbers: G21, G28.