It is well established in the oligopoly theory that the mode of the market competition crucially a§ects the marketís equilibrium outcomes and the social welfare. Singh and Vives (1984) were the Örst to show that the equilibrium market outcomes and the social welfare di§er significantly under alternative types of market competition, namely Cournot (quantity) and Bertrand (price) competition, with the equilibrium prices and profits (quantities, respectively) being higher (lower, respectively) under Cournot competition than under Bertrand, while the Bertrand competition being more e¢ cient in terms of social welfare than the Cournot. Thus, given the signiÖcant market and policy implications that the mode of the market competition has, a substantial economic literature has been developed that examines the robustness of these traditional results under alternative market frameworks. (see among, Cheng, 1985; Vives, 1985; Okuguchi, 1987; Dastidar, 1997; Hackner, 2000). Cheng (1985) provides the geometrical proof of the Sighn and Vives (1984) results, while Okuguchi, 1987 provides the general conditions for comparing the prices under Cournot and Bertrand competition. Further, Vives (1985), examining the Cournot-Bertrand differences in a n-firms oligopoly market with general demand functions, shows that the price-cost margin under Cournot competition is higher than under Bertrand. Dastidar (1997) points out the sensitivity of the Sighn and Vives (1984) results on the market shares rules and demonstrates that they may not be valid under equal sharing and cost asymmetries. More recently, Hackner (2000) investigates the robustness of the Singh and Vives (1984) results under a n-firm oligopoly market structure with vertical product differentiation and shows that the results can not be generalized to the n-Örm case when the products are of sufficiently different quality (i.e., a high quality firm may obtain higher profits under Betrand competition than under Cournot).
Further, the robustness of these cornerstone results in the presence of R&D and innovation firms' strategic investments has been extensively investigated in the economic literature (see among, Delbono and Denicolo, 1990; Qiu, 1997; Symeonidis, 2003; Mukherjee, 2011; Chang and Peng, 2012). In particular, Delbono and Denicolo (1990) show that, under a symmetric and homogenous product duopoly, the Sighn and Vives (1984) results over the welfare can be reversed when firms undertake R&D investments. Furthermore, Qiu (1997) demonstrates that when firms invest in cost-reducing R&D the relevant efficiency of the Cournot versus the Bertrand competition crucially depends on the R&D productivity, the extent of the R&D spillover and the degree of the final market competition. In more details, he shows that Bertrand competition is more efficient than the Cournot, if either R&D productivity is low, or spillovers are weak, or products are sufficiently differentiated, while the opposite holds when R&D productivity is high, spillovers are strong and the products are close substitutes. More recently, Symeonidis (2003) comparing the Bertrand and Cournot equilibria in a differentiated duopoly with substitute goods and product R&D, shows that prices and firms' profits are always higher under quantity competition than under price competition, while, the output, the consumer surplus and the social welfare are higher under Bertrand than under Cournot com- petition when the R&D spillovers are weak or when the products are sufficiently differentiated. The opposite holds when the R&D spillovers are strong and the products are less differentiated. In a different vein, Mukherjee (2011) and Chang and Peng (2012) introducing into the analysis technology licensing show that the traditional results over the Cournot-Bertrand can be efficiently reversed with regard to the innovation levels.