Complexity analysis of dynamic R&D competition between firms

A two-stage duopoly Cournot game model with nonlinear inverse demand function and R&D spillover is established in this paper, and the local stability of the equilibrium points is further analyzed. The complex dynamical behaviors of the built model under different parameters are simulated numerically. The results show that when the speed of adjustment speeds or the degree of R&D spillover exceed a certain range, the Nash equilibrium point will lose stability and the system will enter into a chaotic state. In addition, the global dynamics are analyzed using the basin of attraction, it is found that the system presents path dependency, which implies that the final state of the system is related to its initial state. (c) 2022 Elsevier B.V. All rights reserved.