This chapter introduces the theoretical logic of P-A analysis, and presents the P-S-A model developed specifically to explain strategic interaction in EU enforcement. The chapter is divided into three sections. In the first section, I describe the development of P-A analysis within rational choice institutionalism, and depict its use within economics and political science. The second section provides an in-depth introduction to the generic P-A model, explaining its logic and key components. In the third and final section, I present the triangular P-S-A model, and isolate three basic sets of hypotheses about the conditions that lead the EU’s supranational institutions to pursue private agendas, the scope for supranational influence, and the forms of supervision that the ECJ and the Commission are likely to promote.