Dynamic Analysis Of Stackelberg-Bertrand Game Model

With the prevalence of online shopping and the spillover of talent and technology,new characteristics of market have emerged in recent years.Manufacturers can directly sell products online to consumers(taking on the role of retailers).Retailers can also produce their own products.Selling to consumers(combined with the manufacturer’s functions).Both manufacturers and retailers have dual identities.However,the status of manufacturers and retailers is unequal.This is because manufacturers have long-standing brand prestige and unparalleled long-term technology and experience in the minds of consumers.The set of their price undoubtedly has a huge impact for retailers’ price.Undoubtedly,price decision-making plays a crucial role in competing products for competitive advantage.Looking at the research on market competition at home and abroad,there are many researches on the Cournot model,and there is relatively little research on Bertrand model.Furthermore,the dynamic analysis on the Stackelberg-Bertrand hybrid model is a lack of research conclusions.Therefore,based on the background of oligarch monopoly market,this paper constructs a one Masterone slave and one master-two slave Bertrand model,explores the dynamic evolution of the system,and carries out chaos control,so as to provide a theoretical reference for merchants’ price decision.This article mainly includes the following three aspects of work.(1)Construct a finite-rational master-slave model with a delayed price game model,study the dynamics of the system through stability analysis,and simulate the bifurcation diagram and profit change chart to explore the impact of delay on the system.This helps merchants make decisions using delays.The research results show that: with the increase of merchant price adjustment rate,the two merchants’ prices will have a bifurcation phenomenon and eventually lead to chaos;the delay system and the non-delay system have the same Nash equilibrium;the appropriate delay coefficient can increase the stability of the system.(2)Construct a Bertrand game model with bounded rationality,introduce the delay decision,analyze the dynamic characteristics and stability of the system,and analyze the influence of delay on stability.The results of the study show that proper delay can enhance the stability of the system;on the contrary,improper delay can lead to the original stable system becoming unstable.Therefore,it can not be said that the delay can improve the stability of the system and the stability of the system is alsorelated to the size of the delay coefficient.In addition,more businesses adopting deferred decisions cannot enhance system stability,but also relate to the system’s own structure and other parameters of the system.(3)The chaotic state not only makes the system unstable,but also causes the businesses’ profits to fluctuate drastically and become unpredictable.In order to suppress the adverse effects of chaotic states,this paper adopts a linear control method to control chaos,proposes measures to maintain low-stable product price adjustments,selects appropriate delay weights,and so on,to help merchants adjust chaotic systems to a stable state,thereby to ensure the steady increase in profits.