This paper presents a political economic perspective on inter-judicial conflicts in the EU legal system. The EU legal system is conceptualised as a multi-level, non-hierarchical court system, in which upper and lower-level courts do not only respond to each other’s moves but also to the behaviour of non-judicial actors. This theoretical framework is then used to discuss several puzzles arising from the jurisprudence of constitutional conflict: the capacity of national courts to influence the Court of Justice, the existence of disparities among them in that respect, and the risk that domestic actual episodes of judicial non-compliance may pose to the existence of the EU legal order. It is argued that many key aspects of the “jurisprudence of constitutional conflict” – and, in particular, the tug of war between the Court of Justice and the German Federal Constitutional Court – can be aptly captured by a simple Hawk-Dove game. At the same time, though, domestic supreme and constitutional courts are shown to differ widely in their capacity to exert influence on the Court of Justice’s policymaking.