This book studies the strategic policy interactions in a monetary union. The leading protagonists are the European Central Bank and national governments. The target of the ECB is low inflation in Europe. The targets of a national government are low unemployment and a low structural deficit. There are demand shocks, supply shocks, and mixed shocks. There are country-specific shocks and common shocks. This book develops a series of basic, intermediate, and more advanced models. Here the focus is on the Nash equilibrium. The key questions are: Given a shock, can policy interactions reduce the existing loss? And to what extent can they do so? Another topical issue is policy cooperation. To illustrate all of this there are a lot of numerical examples.