Research On The Bertrand Chaotic Games With Two Time Delays

With the rapid development of social economy and the frequent mergers and acquisitions,more and more markets walks into the era of oligopoly,and the competition of various enterprises in the market is mainly reflected in the price competition,but the existing related research is most aimed at introducing a time delay for duopoly market,but the market research for two time and more delay is less,and the research method also has certain limitation,so it is necessary for us to analyze the complexity of the duopoly market's price competition with two time delay,and to establish the corresponding price game system to guide the enterprise's development,among them,to analyze the complexity is one of the main research methods in the nonlinear economy system.This paper mainly completed the following work:1.Two time delays are introduced into the duopoly price game model,and the Nash equilibrium stability domain of the model is given.Market were analyzed in detail by numerical simulation to find that how the number of decision makers and delayed parameters influence the stability domain and corporate profits,and the study found that delaying decisions of firms increase the number of not only the stability domain of Nash equilibrium,but also bring the cumulative average profits increase,and the expand of the delay parameters will increase the Nash equilibrium stability domain,and it will also reduce the cumulative average profit of the enterprise,so enterprises should adopt delay decisions in oligopoly market,and select delay parameters appropriately.2.In order to be more in line with the actual situation,model should consider factors such as the asymmetry product replacement,and the limited rational decision.On this basis,the article analyzed the complexity of the model,and obtained the stability domain of Nash equilibrium,and studied by numerical simulation to find how the price adjustment speed influence the enterprise profit,the influence of equilibrium cycle etc.We found that when any enterprise in the market changes price too fast will lead to chaos system,and make the corporate profits in the system was unable to achieve steady growth and prolong the time of the enterprise to reach a balanced cycle.Based on this,the article also adopted delayed feedback control method to accomplish control of chaotic state of three monopoly price game system.3.The chaotic state not only affects the price decision making of corporate,but also make the corporate profits fluctuate wildly,and make it hard to be predicted.Therefore,in order to restrain and eliminate the influence of chaotic state,this paper uses delay feedback control method and linear control method to carry on the effective control of the chaos state of the two models.And it put forward several measures which can help enterprises to implement feedback control: for example,to control the product price adjustment speed,to reduce the product replacement rate,to reduce the marginal cost,to choose the appropriate delay weight coefficient,etc.All these will help the system to restore the steady state of enterprise profit growth.