We utilise a standard reduced‐form neo‐Keynesian model in a monetary union, in which the monetary authority and the fiscal authorities strategically interact, to explore who, under alternative institutional arrangements (strategic and fiscal regimes) and shocks' configurations, bears the burden of asymmetric shocks' stabilisation. We show that in the core/periphery fiscal regime, described by an asymmetry in the sequence of moves between the core and the peripheral member‐states, asymmetric shocks pass through at the union level to the inflation rate and the output gap when there are strategically significant spill‐over effects and the monetary policy's and fiscal policies' instruments are not perfect substitutes in the stabilisation process. The monetary authority reacts to asymmetric shocks, but does not succeed in fully offsetting them. The first best implies the coordination of fiscal policies. A second best embraces the fiscal leadership strategic regime (as a form of implicit coordination), when there are strong interconnections in the union, or the use of policy instruments by the fiscal authorities that directly decrease inflation when fiscal policy is expansionary, such as taxes, production subsidies or public investment, when there is a strong cost channel of monetary policy.