Europe is oscillating between increased integration and permanent risk of dissolution. In this framework, one often debates the role of bilateral relations, with the following question: does bilateralism foster or delay overall co-operation? We address this question in an experimental framework where we study the behaviour of agents who are confronted with a multiplicity of prisoners' dilemma games, either in a bilateral or a multilateral way. We surprisingly observe that the co-operation between all is significantly higher when interactions are bilateral and that the difference between these two institutional contexts is growing in time in favour of bilateralism.