We consider a differentiated duopoly where firms invest in research and development (R&D) to reduce their production cost. The objective of this study is to derive and compare Bertrand and Cournot equilibria, and then examine the robustness of the literature's results, especially those of Qiu (1997). We find that The main results of this study are as follows: (a) Bertrand competition is more efficient if R&D productivity is low, industry spillovers are weak, or products are very different. (b) Cournot competition is more efficient if R&D productivity is high and R&D spillovers and products' degree of substitutability are not very small. (c) Cournot competition may lead to higher Outputs, higher consumer surpluses and lower prices, provided that R&D productivity is very high and spillovers and degree of substitutability of firms' products are moderate to high, (d) Cournot competition results in higher R&D Investments compared to Bertrand's. These results show that the relative efficiencies of Bertrand and Cournot equilibria are sensitive to the suggested specifications, and hence far from being robust.

We consider a differentiated duopoly where firms invest in research and development (R&D) to reduce their production cost. We show that if the firms play a one stage game, i.e., they choose R&D and price (in Bertrand game) or quantity (in Cournot game)at the same time, then the usual result stating that Bertrand competition is more efficient than Cournot competition still holds.

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 spillovers 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.