This paper analyzes the interaction between monetary and macroprudential policies mainly in the context of the non-cooperation among policy authorities. Each policy authority’s optimal response is to tighten its policy measures when other authorities’ policy measures are loosened. This indicates that the two policies are substitutes for each other. This result still holds when an additional financial stability mandate is assigned to the central bank. The condition for the response functions to converge to a Nash equilibrium state is analyzed along with the speed of convergence, showing that they depend on the authorities’ preferences and the number of mandates assigned to policy authorities. If the financial supervisory authority (FSA) assigns greater importance to the output gap or a stronger financial stability mandate is assigned to the central bank (CB), the probability of nonconvergence increases and the speed of convergence declines even when the condition of convergence is satisfied. Meanwhile, if the CB considers output stability as an important task, the probability of convergence and the speed of converging to a state of equilibrium are high. Finally, when a single mandate or small number of mandates is/are assigned to each authority, stability is more quickly restored as compared to when many mandates are assigned.