We consider a two-stage R & D then output or price duopoly game in which R & D spills over, so reducing the marginal cost of both the investing firm and its rival. We compare the non-cooperative regime to three collusive regimes: joint venture (collusion on R & D), price fixing (collusion at the price or output stage) and merger (collusion at both stages) and evaluate under what circumstances a collusive regime improves welfare. If spillovers are sufficiently large, all three regimes are beneficial, although mergers are more likely, and price-fixing less likely to produce specific benefits than are joint ventures.