WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Complexity and Control of a Cournot Duopoly Game in Exploitation of a Renewable Resource with Bounded Rationality Players
Authors: ,
Abstract: Based on the related literatures, a new dynamic Cournot duopoly game model in exploitation of a re- newable resource with bounded rationality players is built up. The local stable region of Nash equilibrium point is obtained through using the theory of bifurcations of dynamical systems. It is found that increasing the output ad- justment speed parameters of the system can affect the stability of Nash equilibrium point and lead chaos to occur. Its complex dynamics is demonstrated by the way of plotting the bifurcation diagrams, computing and plotting the Lyapunov exponents, plotting phase portraits and calculating the fractal dimension. Furthermore, the chaos can be respectively controlled by making use of the straight-line stabilization method, parameters adjustment method and time-delayed feedback method. The derived results have important theoretical and practical significance to the exploitation of renewable resource.