In this paper, we examine how the structure of an imperfectly competitive input market affects final-good producers? incentives to form a Research Joint Venture (RJV), in a differentiated duopoly where R&D investments exhibit spillovers. Although a RJV is always profitable, downstream firms? incentives for R&D cooperation are non-monotone in the structure of the input market, with incentives being stronger under a monopolistic input supplier, whenever spillovers are low. In contrast to the hold-up argument, we also find that under non-cooperative R&D investments and weak free-riding, final-good producers invest more when facing a monopolistic input supplier, compared with investments under competing vertical chains. Integrated innovation and competition policies are also discussed.