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We consider a dynamic game model of a two-country monetary union. Governments (fiscal policies) pursue national goals while the common central bank’s monetary policy aims at union-wide objectives. For a symmetric demand shock, we derive numerical solutions of the dynamic game between the governments and the central bank. We consider conflicting (non-cooperative Nash equilibrium) and coordinated policy-making (cooperative Pareto solutions). We show that there is a trade-off between the deviations of instruments and targets from desired paths; the volatility of output and inflation increases when private agents react more strongly to changes in actual inflation.