This paper considers an economy where central-bank-issued fiat money competes with privately issued e-money. We study a policy-setting game between the central bank and the e-money issuer and find (1) the optimal monetary policy of the central bank depends on the policy of the private issuer and may deviate from the Friedman rule; (2) multiple equilibria may exist; (3) when the economy approaches a cashless state, the central bank’s optimal policy improves the market power of the e-money issuer and can lead to a discrete decrease in welfare and a discrete increase in inflation; and (4) first best cannot be achieved.