Well before the global financial crisis, the long-term trend in fiscal policy had raised concerns about risks for the outcomes of monetary policy. Are fears of an unpleasant monetarist arithmetic justified? To provide some insights, this paper examines strategic fiscal-monetary interactions in a novel game-theory framework with asynchronous timing of moves. It generalizes the standard commitment concept of Stackelberg leadership by making it dynamic. By letting players move with a certain fixed frequency, this framework allows policies to be committed or rigid for different periods of time. We find that the inferior non-Ricardian (active fiscal, passive monetary) regime can occur in equilibrium, and that this is more likely in a monetary union due to free-riding. The bad news is that, unlike under the static commitment of Sargent and Wallace (1981), this may happen even if monetary policy acts as leader for longer periods of time than fiscal policy. The good news is that under some circumstances an appropriate institutional design of monetary policy may not only help the central bank resist fiscal pressure and avoid the unpleasant monetarist arithmetic, but also discipline excessively spending governments. By acting as a credible threat of a costly policy tug-of-war, long-term monetary commitment (e.g. a legislated inflation target) may induce a reduction in the average size of the budget deficit and debt, and move the economy to a Ricardian (passive fiscal, active monetary) regime. More broadly, this paper demonstrates that our game-theoretic framework with dynamic leadership can help to uniquely select a Pareto-efficient outcome in situations with multiple equilibria where standard approaches do not provide any guidance.