Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

R&D Investment Competition and Efficiency in a Mixed Duopoly Model, with Endogenous Spillover

In this paper, a mixed duopoly model is used to explain how ownership structure influences the innovation performances of firms. A three stage-game is adopted in the study. In first stage, firms make R&D expenditure which leads to a profit increasing; in the second stage, firms choose the level of technological improvement they would like to share with the rival; and production quantity will be decided in the final stage. The theory explains that as long as public firms continue their dual roles as productive entities and social safety nets, they cannot be purely profit-oriented, and continue to have poor innovation performance.