In this paper the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behaviour. Differential games are used in the framework of a continuous-time econometric model of the Italian economy. The Nash and the Stackelberg non-cooperative equilibrium solutions are computed, and the case for cooperation is analysed by considering the Nash and the Kalai-Smorodinsky bargaining models. It is shown that, in the Italian case, the government has a stronger bargaining position than the central bank. A comparison is then made between the different solutions to show that the drawbacks that emerge from non-cooperation are not simply those depending on the players' payoffs. Other features are in fact considered which constitute a further argument for policy co-ordination.