Abstract
According to a dynamical multiteam Cournot game in exploitation of a renewable resource, a new dynamic Cournot duopoly game model with team players in exploitation of a renewable resource is built up in this paper. Based on the theory of bifurcations of dynamical systems, the stability of the system is studied and the local stable region of Nash equilibrium point is obtained. The effect of the output adjustment speed parameters and the weight parameter of the system on the dynamic characteristics of the system are researched. The complexity of the system is described via the bifurcation diagrams, the Lyapunov exponents, the phase portrait, the time history diagram, and the fractal dimension. Furthermore, the chaos control of the system is realized by the parameter adjustment method. At last, an evolutionary game as a special dynamic system is constructed and analyzed which is more useful and helpful in application. The derived results have very important theoretical and practical values for the renewable resource market and companies.
Highlights
Chaos has become a hot topic in the competition of oligarchs
Reference [4] studied the chaotic dynamics in nonlinear duopoly game with bounded and naive players
Reference [6] studied the dynamical behaviors of a duopoly game with delayed bounded rationality and obtained some practical and theoretical significance in the practice
Summary
Chaos has become a hot topic in the competition of oligarchs. Research on the complexity of the oligopoly game model has been paid attention to by researchers and scholars recently. Reference [1] studied different strategies which are the Cournot model, the Stackelberg case, and the dynamic system of a duopoly game and investigated stable equilibrium point, cycles, bifurcation, and chaos of the systems. Reference [2] obtained the explicit stability zones for Cournot game with 3 and 4 competitors, and [3] analyzed the stability, bifurcation, chaos, and chaos control of a Kopel model. Reference [8, 9] made the analysis on the complexity of a Cournot-Bertrand duopoly game model with limited information and introduced a 4D Hyperchaotic System, making the numerical simulation and achieving a second control. Reference [19] mainly established a dynamical multiteam Cournot game in exploitation of a renewable resource and analyzed the asymptotic stability of the equilibrium solution of the game.
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