this work, we investigate a Cournot-Bertrand duopoly model with product differentiation between two different firms, where one company uses price as decision variable and the other quantity. The stability of Nash equilibrium point is investigated, role parameters on studied. It shown that system experiences three types bifurcations when go through boundary curves region. Furthermore, model's bi...

In this study, we give a new curve pair that generalizes some of the famous pairs curves as Bertrand and constant torsion curves. This is defined with help vector obtained by intersection osculating planes such makes same angle $\gamma$ tangents We examine relations between torsions curvatures these mates. Also, have seen unit quaternion corresponding to rotation matrix Frenet vectors $q=\cos (...

This paper provides a simple model of endogenous horizontal product differentiation that has two important implications. First, the model can explain the “empirical Bertrand paradox” – the failure to observe homogeneous product Bertrand oligopoly. If product differentiation is possible at reasonable cost, then Bertrand firms would always invest in product differentiation. Using a quadratic util...

This paper compares Bertrand and Cournot equilibria in a di®erentiated duopoly with R&D (research and development) competition. Cournot competition is shown to induce more R&D e®ort than Bertrand competition. However, the price is lower and output is higher in Bertrand than in Cournot competition. Furthermore, the Bertrand equilibrium is more e±cient than the Cournot equilibrium if either R&D p...

Alternative market structures are distinguishable by the degree of parallel action exhibited by producers. We show that the correlation between output levels varies systematically with the degree of interdependence among firms, and establish an ordering among alternative behavioral hypotheses (Cournot, Stackelberg, Edgeworth/Bertrand, collusion, and perfect competition). Because the ordering is...