Using an inifinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria, for a differentiated duopoly engaging in process R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low, or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes and spillovers are not close to zero. This last result is different from what has been obtained in the literature.
This shows hence that considering a dynamic model and more general investment costs do have an impact on efficiency results.