Dynamic Analysis And Numerical Simulation Of Nonlinear Game Model Based On Taxation And Subsidy

Since China joined WTO in 2001,the scale of foreign trade has been enlarged and a large number of foreign enterprises have been poured into the domestic market.However,based on the national conditions of our country,it is not allowed that anti-dumping investigation can be applied to the foreign enterprises.As a result,some fledgling enterprises at home suffer from substantial threats.Therefore,aiming at the game analysis with respect to the policies has become one of the most important issues,that is,the foreign enterprises are taxed and domestic enterprises are subsidized by the domestic government.In the context of the government carries out polices to domestic and foreign enterprises producing heterogenous goods,in this paper,a quadratic cost function is introduced and a duopoly game model is established.Meanwhile,the optimal policy of maximizing social welfare under different polices is analyzed by means of game theory,nonlinear dynamics and chaos theory.According to the optimal policy,the evolution rules of dynamic game model with output and price competing among enterprises are shown.The main contents are as follows:1.On the basis of three kinds of polices implemented by the domestic government?taxing on foreign firm,subsidizing to domestic firm,the combination of taxing on foreign firm and subsidizing to domestic firm?,the game model about output and price competition is established.By using backward induction and numerical simulation,the relationship between social welfare under the three policies is analyzed.The results show that the combination of tax and subsidy is the optimal policy.2.Based on the background that the government carries out the optimal policy,enterprises compete with output and bounded rational expectation is introduced,leading to the establish-ment of the dynamic game model.As a result,the local asymptotic stability of equilibrium point is analyzed,and the impact of taxation and subsidy share on the stable region of Nash equilibri-um point is exhibited in the two parameters space phase diagram.At the same time,the direction of Flip bifurcation at Nash equilibrium point is deduced by means of central manifold theorem and paradigm theory.The complex dynamic behavior involved in the system is depicted by taking advantage of numerical simulation.The results show that when the output adjustment speed increases,the state of the system enters chaos via Flip bifurcation,corresponding to the deceasing trend of the profit curve.Instead,when the subsidy or taxation share increases,both of them can lead to the increase of the profit curve of the domestic enterprises as well as the de-crease of the profit curve of the foreign enterprises.On the other hand,the time series diagram and phase diagram are used to discuss PM-III intermittent chaos and crisis-induced intermittent chaos.PM-III intermittent chaos is described by the alternation of 6-period and chaotic motion-s,and crisis-induced intermittent chaos is described by the collision between the weak chaotic attractor collides and the unstable periodic orbit in the basin of attraction,which expands the range of motion.The coexistence of attractor is also explored in the terms of the two parameters space phase diagram,indicating the system has strong path dependence.3.Based on the background that the government carries out the optimal policy,enterprises compete with price and bounded rational expectation is introduced,leading to establishment of the dynamic game model.The qualitative behavior of the model is analyzed by relying on the knowledge of nonlinear dynamics.With the help of 1-D bifurcation diagram,1-D largest Lyapunov exponent diagram,time series diagram,phase diagram,2-D parameters space phase diagram and 2-D largest Lyapunov exponent diagram,the complex evolutionary process of the system with different parameters varying is visualized.The results show that when the price adjustment speed₄)increases,firstly,the state of the system enters chaos via either Flip bi-furcation or twice mappings Neimark-Sacker bifurcation;secondly,the fractal structure of the attractor is much cleaner with the fractal dimension increasing;thirdly,by introducing the state feedback and parameter adjustment control strategy,the speed of the system entering chaos is delayed and the stable region of equilibrium point is expanded;at last,in virtue of the critical line to describe the internal structure of the basin of attraction contacting,holes in the basin of attraction appear.Additionally,when the subsidy shareincreases,the price and profit bifur-cation diagram take on the backward Flip bifurcation,which is beneficial to the stability of the system;when the taxation shareincreases,the price and profit bifurcation diagram is covered with twice mappings Neimark-Sacker bifurcation,resulting in the tendency of the system en-tering chaos.