This paper analyses the consequences for monetary policy arising from private, centralised digital currencies such as Alipay or Facebook's Libra. Firms introduce private currencies to generate information on consumers and seignorage revenues. The paper highlights three important results. First, information shapes the degree of currency competition as firms do not accept their competitors' currencies. Second, producers issuing private currency implement a variant of the Friedman rule. To maximise the sum of product profits and seignorage revenues, they either set private currency interest rates to zero or give compensating product discounts. Public currency is unable to compete unless the central bank sets their interest rate to zero, resulting in deflation. Third, inflationary pressures arise if firms form currency consortia but decision powers and seignorage claims are concentrated in the hands of one firm.