This paper studies noncooperative games between a monetary authority and a macroprudential regulator whose objectives are a subset of those in the social loss function. The analysis is based on a New Keynesian model with a financial sector and a financial friction à la Gertler and Karadi (2011). When the friction affects the financing of all factors of production equally, macroprudential policy is shown to be a powerful additional tool, fully eliminating inefficiencies, regardless of the source of the shock and no matter whether the central bank and the regulator cooperate. But when trade‐offs are present and policy is discretionary, the institutional arrangements become crucial. While coordination leads to higher welfare than a setting in which each authority takes the decision rule of the other as given (namely, the Nash equilibrium), our analysis shows that a noncooperative setting in which the macroprudential authority acts as a leader within the period can be superior to cooperation. Finally, our conclusions are unaffected by whether the macroprudential instrument affects funding costs or acts as a liquidity requirement.