Complexity Analysis And Chaos Control For The Oligopoly Price Game Model Based On Time-delay Decision

The rapid development of social economy and the frequent reorganization ofcompanies lead to that more and more markets are stepping into oligopoly market,and the competition in these markets is reflected in price. What’s more, fewresearches about the markets with three or more oligarchs have existed now, and theirresearch methods have limitations, therefore it’s important and necessary to study theprice competition in the oligopoly markets with three or more oligarchs by complexityanalysis, and dynamic systems can be established to guide the development of thosecompanies. By the way, complexity analysis is the mainstream research method ofnonlinear economic systems. The main content of this dissertation is as follows:First, we establish a price game model in triopoly market, and in order to be moreclose to the reality many factors such as non-symmetrical product substitutions,bounded rationality have been considered in this model. On this basis, we point outthe stable region of Nash equilibrium, and simulate the effects of price adjustmentspeed to the price, profit and period of companies. We discovered that no matter anyoligarch’s price adjustment speed is too fast, the system will fall into chaos, andcompanies in chaos can’t increase their profits and will cost more periods to reachequilibrium. At last, we realized the chaos control of this system via Delay FeedbackControl.Second, for further close to reality time delay decision has been brought in theprice game model of triopoly market, and we point out the stable region of Nashequilibrium. We analysis how the number of delay decision makers and the delayparameter affect system stability and those oligarchs’ profit. We discover that moredelay decision makers will not impact the system stability, but can lead to thoseoligarchs’ higher cumulative profits. And the increasement of delay parameters canexpand the stable region of Nash equilibrium, but will reduce the average cumulativeprofits of oligarchs. So all oligarchs in triopoly markets should apply delay decisionwith appropriate delay parameter.Third, price game model in four-oligarch market has been established, and wefound the applying of delay decision can also result in higher average cumulativeprofits in this kind of market. On this basis, we analysis how the price adjustment spend and delay parameters change the system stability and those oligarchs’ profits,and we have similar conclusions with triopoly markets. Meanwhile, only applying theDelay Feedback Control to the chaos-creating oligarchs can realize the chaos controlof this system, or it will be invalid.