Abstract
Based on the oligopoly game theory and the intellectual property rights protection policy, we investigate the complex dynamical behaviors of a mixed duopoly game with quadratic cost. In the new system, a few parameters are improved by considering intellectual property rights protection and the stability conditions of the Nash equilibrium point are discussed in detail. A set of the two-dimensional bifurcation diagrams is demonstrated by using numerical modeling, and these diagrams show abundant complex dynamical behaviors, such as coexistence of attractors, different bifurcation, and fractal structures. These dynamical properties can present the long-run effects of strengthening intellectual property protection.
Highlights
A large number of research works about the duopoly game have been investigated
Many scholars focus their attention on the complex dynamical behaviors of the duopoly game model [1,2,3,4], duopoly game with long-memory effects [5], R&D competitions with spillover [6], and some new investigation in the R&D evolution network model with spillover [7, 8]
Barbu and Militaru [24] investigate the moderating effect of intellectual property rights on relationship between innovation and company performance in the manufacturing sector, and the findings indicate a positive correlation between patenting and new ventures’ growth, access to venture capital, and new knowledge. e conceptual model was analyzed using hierarchical linear regression with company performance as the dependent variable and innovation potential, patent rights, copyrights, trademarks, and trade secrets as independent variables
Summary
A large number of research works about the duopoly game have been investigated. At is to say, executing intellectual property rights protection in the developing countries could improve welfare of the world. Billette de Villemeur et al [18] built a model aiming at simulating dynamical competition among pharmaceutical enterprises under the frame of intellectual property rights. When roles of enterprise are predetermined, the social welfare under protection of intellectual property is greater than that of endogenous innovation, which illustrates the significance of dynamic competition. Chu [19] indicates the significance of that pharmaceutical intellectual property rights protection in drug regulatory process. It could take positive effect on encouraging drug innovation and marketing so as to increasing social welfare in health service.
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