Dynamic model of R&D, spillovers, and efficiency of Bertrand and Cournot equilibria

Using an inFInite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of 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 spill-overs are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.