Dynamic behaviors in a Cournot duopoly model with knowledge spillover effect based on constant conjectural variation

Abstract

On the basis of constant conjectural variation, a static Cournot duopoly model is built first in this paper, where the effects of knowledge spillover and product differentiation have been parameterized. Through the first order conditions, we can obtain the static conjectural variation equilibrium. By using the gradient adjustment mechanism, a dynamic conjectural variation model, represented by a two-dimensional difference equation, is established, in which two firms have bounded rationality. Then, the local stability of the Nash equilibrium is analyzed. From further studies on the effects of conjectural variation to the dynamics of the established model, we conclude that the more intense the market competition, the bigger the size of the stability region. In general case, the two axes are invariant sets, while the diagonal line is also an invariant set in symmetric case. Through the method of numerical simulation, we can deeply understand the complex characteristics of dynamic behaviors and the means for economic activities. Finally, synchronized behaviors are also studied by the method of critical curves and basins of attraction.