In this paper we argue that if monetary policy has insufficient deflation, private agents have incentives to set up alternative payment systems like fractionally backed bank deposits, which pay interest on the means of payment. In a competitive environment with free entry, these alternative systems are inherently fragile in the sense that they are subject to socially costly bank runs. These social costs are not internalized by private individuals and banks and may exceed their social benefits. We argue that as communication technologies improve, the social benefits of fractional reserve banking decrease, but the private benefits may still exceed the private costs so that such systems continue to be used. In such situations, 100% reserve requirements are optimal.