Complex Dynamics Analysis Of Two-Stage Game Model Based On Advertisement Spillover Effect

With the rapid development of economy,the amount of advertising investment of manufacturers increases gradually.Manufacturers will start from their own interests when formulating advertising strategies,which leads to the incomplete consideration of strategy formulation and always makes the advertising promotion fail to meet the predetermined expectations.Therefore,manufacturers should fully consider the influence of the market on the advertising strategy when formulating the advertising promotion strategy.There is a certain correlation between the products produced by the two manufacturers,which leads to the spillover effect when the manufacturers promote their products through advertising,which to some extent affects the profit expectation that the manufacturers want to achieve through advertising promotion.Therefore,in order to make the most effective advertising investment to promote product sales,manufacturers should fully consider the spillover effect when formulating advertising strategies to maximize the benefits.This is also the main content of this thesis.In the context of symmetric and asymmetric market information,based on limited rationality,a two-stage game model with completely uncooperative and partially cooperating games with advertising spillover effects is established.The research focuses on the effects of parameters such as advertising spillover effects,advertising burden rates,and adjustment speed on system behavior,and provides a certain theoretical basis for the decision-making of complementary product manufacturers' advertising investment in market competition.The main research contents of this article are as follows:1.Under the background of advertising spillover effect,based on the theory of bounded rationality and nonlinear dynamics,a two-stage game model with advertising spillover effect is established by taking the amount of advertising input of two manufacturers and the quantity of product demand as decision variables.Among them,the decision-making of the manufacturer's game behavior is divided into two stages: the competition of advertising investment and the competition of product price.Firstly,the types of equilibrium points are discussed according to the stability theory of equilibrium.Secondly,the conditions for Flip bifurcation and Neimark-sacker bifurcation at Nash equilibrium were obtained by the analysis of the Jury condition.Finally,the influence of single parameter and double parameter on the local stability and dynamic behavior of the system was studied by numerical simulation of MATLAB software,and the maximum Lyapunov index corresponding to its bifurcation diagram was simulated,and the phenomenon of the system bifurcation from Flip to chaos was verified.2.This paper focuses on the two-stage game model under the condition of market information symmetry and the condition of complete non-cooperation and partial cooperation between two manufacturers.The double parameter bifurcation diagram and single parameter bifurcation diagram as well as the corresponding maximum Lyapunov exponential diagram were obtained by numerical simulation with different overflow effects and adjusting velocity are selected to show the periodic and chaotic repeated dynamic behavior of the system and finally return to chaos.In addition,the stable domain of Nash equilibrium points obtained is not the same.When the adjustment speed of advertising spillover effect is no longer in the stable domain,slight changes will cause unpredictable fluctuations in the market and make the market become chaotic.The existence of attractor coexistence in the system is explained by numerical simulation,and the attractor basin is used to explain the phenomenon.3.This paper focuses on the two-stage game model of two manufacturers in the case of partial advertising cooperation under the condition of market information asymmetry.Numerical simulation shows the evolution process of advertising spillover effect and advertising sharing rate.The two-parameter bifurcation diagram and the corresponding stable domain clearly show the motion state of the system.The single-parameter bifurcation diagram and the maximum Lyapunov exponential diagram analyze the influence of advertising spillover effect on the system under asymmetric information.The phase diagram describes the evolution process of attractor.