We highlight conditions under which R&D agreements may harm consumers by increasing final prices. This occurs although members of the R&D agreement increase their R&D efforts. We focus on cases where firms compete both on the final market and to buy an input necessary for R&D. The market is composed of a competitive fringe and two strategic firms that enjoy a first mover advantage on both markets. By increasing its R&D input purchase, a strategic firm increases the cost of all its rivals and in particular deters entry in the fringe. This reduces downstream competition and increases the final price. Therefore, an R&D agreement may induce strategic overbuying of R&D input by members of the agreement at the expense of rival firms and consumers.