Abstract
In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.
Highlights
On account of the complexity of oligopoly market setting, many authors are committed to studying the structure of oligopoly market
Cavalli and Naimzada [13] analyzed the complex dynamical behaviors of the built nonlinear game model when the equilibrium point loses its stability, and the coexistence of multiple attractors is found in their research
The local stability and the complex dynamical behaviors of the given system are discussed through the analytical method and numerical method
Summary
On account of the complexity of oligopoly market setting, many authors are committed to studying the structure of oligopoly market. Cavalli and Naimzada [13] analyzed the complex dynamical behaviors of the built nonlinear game model when the equilibrium point loses its stability, and the coexistence of multiple attractors is found in their research. The dynamical behavior of the mixed duopoly model composed of public-private joint venture and private enterprise is analyzed, in which the publicprivate joint venture takes the payoff of government into its objective function. We assume that these two enterprises produce homogeneous products.
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