We develop a model of strategic networks in order to analyze how trade unions will affect the stability and efficiency of R&D collaboration networks in an oligopolistic industry with three firms. Whenever firms settle wages, the complete network is always pairwise stable and the partially connected network is stable if and only if spillovers are large enough. If spillovers are small, the complete network is the efficient network; otherwise, the efficient network is the partially connected network. Thus, a conflict between stability and efficiency may occur: efficient networks are pairwise stable, but the reverse is not true. Strong stability even reinforces this conflict. However, once unions settle wages such conflict disappears: the complete network is the unique pairwise and strongly stable network and is the efficient network whatever the spillovers.