The European Social Dialogue (ESD) is a mixed story of ongoing negotiations between the social partners but with rather few binding agreements. Whereas some see the sparse actions as an inevitable consequence of deep structural and political asymmetries, others have pointed out the key role played by the Commission, as a “shadow of hierarchy”, in pushing the social partners towards binding agreements. By applying novel insights from theories of veto players and asymmetric interdependence to an in-depth case study of two agreements, the article is the first attempt to take a systematic game theoretical approach to the study of the ESD. We show that the likelihood of a binding agreement depends on the degree and changeability of the shadow of hierarchy as well as the complexity of issue and reputational risks of the social partners. The findings have implications for the likely effectiveness of the recent attempt to “re-launch” the ESD.