Given the increasing interdependence of both financial systems and attendant payment and settlement systems a vital question is what form should optimal policy take when there are two connected payment systems with separate regulators.

In this paper I show that two central banks operating in a non-cooperative way will not have an incentive to achieve the optimal allocation of goods. I further show that this non-cooperative outcome will be supported by a zero intraday interest rate and constant fixed exchange rate. This is in contrast to recent research; which has shown that domestically a zero intraday interest rate will achieve a social optimum and that the central bank has an incentive to achieve it.