We present a model of R&D with endogenous spillovers and demonstrate that noncooperation can produce maximal spillovers. The only other noncooperative outcome is minimal spillovers. When noncooperation achieves maximal spillovers so does an RJV, whereas minimal noncooperative spillovers imply partial—but not necessarily maximal—spillovers by an RJV. Partial RJV spillovers are chosen for anti-competitive reasons and an RJV may also close a lab for anti-competitive reasons. The possibility of anti-competitive outcomes is precluded in the existing literature on RJVs which focuses on symmetric outcomes. Our model predicts when anti-competitive behaviour by an RJV arises.