scholarly journals Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ting Li ◽  
Dongyun Yan ◽  
Xiaogang Ma
Keyword(s):  
Chaos Control ◽  
Stable Region ◽  
Game Model ◽  
Parameter Adaptation ◽  
Nash Equilibrium Point ◽  
Price Game ◽  
The Stability ◽  
Adaptation Method ◽  
Bifurcation Chaos

With application of nonlinear theory, this paper makes study on the long-term competition in a recycling price game model by manufacturers and retailers. The paper makes analysis on the local stability of the Nash equilibrium point and gives the corresponding stable region. It has been found that the stability of the whole system would be significantly impacted by the following factors which include adjustment speed of the recycling price, the proportion of recycled products by channels, the sensitivity of consumers for the recycling price, and the price cross-elasticity between two channels. By means of the simulation technology, the complexity of the recycling price in the system in the long-term competition has been demonstrated. Owing to the change of parameters, bifurcation, chaos, and other phenomena would appear in the system. When the system is becoming chaotic, the profit of the whole system decreased. All these show that the operational efficiency for the whole system will be impaired by the chaos. Effective chaotic control of the system will be realized by the use of the parameter adaptation method.

scholarly journals Chaotic Characteristics and Application of Cooperative Game and Evolutionary Game

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yujing Yang ◽  
Junhai Ma ◽  
Hongliang Tu
Keyword(s):  
Chaos Control ◽  
Evolutionary Game ◽  
Time History ◽  
Renewable Resource ◽  
Stable Region ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Cournot Game ◽  
Adjustment Speed ◽  
The Stability

According to a dynamical multiteam Cournot game in exploitation of a renewable resource, a new dynamic Cournot duopoly game model with team players in exploitation of a renewable resource is built up in this paper. Based on the theory of bifurcations of dynamical systems, the stability of the system is studied and the local stable region of Nash equilibrium point is obtained. The effect of the output adjustment speed parameters and the weight parameter of the system on the dynamic characteristics of the system are researched. The complexity of the system is described via the bifurcation diagrams, the Lyapunov exponents, the phase portrait, the time history diagram, and the fractal dimension. Furthermore, the chaos control of the system is realized by the parameter adjustment method. At last, an evolutionary game as a special dynamic system is constructed and analyzed which is more useful and helpful in application. The derived results have very important theoretical and practical values for the renewable resource market and companies.

scholarly journals Complexity Analysis of a Triopoly Cooperation-Competition Game Model in Convergence Product Market

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Liming Zhao ◽  
Xiaofeng Liu ◽  
Ning Ji
Keyword(s):  
Local Stability ◽  
Control Method ◽  
Complexity Analysis ◽  
Product Market ◽  
Stable Region ◽  
Price Strategy ◽  
Game Model ◽  
Feedback Control Method ◽  
Complex Relationships ◽  
Bifurcation Chaos

This work considered a tripartite cooperation-competition game model for the convergence product market, whose products are compounds of two base products or services. An early convergence product firm monopoly in this market and two potential entrants from the base products decide to cooperate with another to compete with the monopolist. We analyzed factors that affect existence and local stability of the Nash equilibrium. Rich nonlinear dynamic behaviors like bifurcation, chaos, and attractors are presented to explain the complex relationships between the three players. Results showed that the pulling effect on profit for the united R&D activity can significantly enlarge the stable region. Too frequently adjusted price strategy will bring the system into chaos. A parameter feedback control method is given to control the chaotic system and we numerically verified its effectiveness. This study has significant values to understand the fluctuations in related convergence product market.

scholarly journals Dynamic Investigation in Green Supply Chain considering Channel Service

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Qiuxiang Li ◽  
Mengmeng Li ◽  
Yimin Huang
Keyword(s):  
Supply Chain ◽  
Dynamic System ◽  
Attraction Domain ◽  
Green Supply Chain ◽  
Game Model ◽  
Supply Chain System ◽  
Parameter Adaptation ◽  
Chain System ◽  
Adaptation Method ◽  
Channel Service

Considering firm’s innovation input of green products and channel service, this paper, in dynamic environment, studies a dynamic price game model in a dual-channel green supply chain and focuses on the effect of parameter changing on the pricing strategies and complexity of the dynamic system. Using dynamic theory, the complex behaviors of the dynamic system are discussed; besides, the parameter adaptation method is adopted to restrain the chaos phenomenon. The conclusions are as follows: the stable scope of the green supply chain system enlarges with decision makers’ risk-aversion level increasing and decreases with service value increasing; excessive adjustment of price parameters will make the green supply chain system fall into chaos with a large entropy value; the attraction domain of initial prices shrinks with price adjustment speed increasing and enlarges with the channel service values raising. As the dynamic game model system is in a chaotic state, the profit of the manufacturer will be damaged, while the efficiency of the retailer will be improved. The system would be kept at a stable state and casts off chaos by the parameter adaptation method. Results are significant for the manager to make reasonable price decision.

scholarly journals Complexity Analysis of a 3-Player Game with Bounded Rationality Participating in Nitrogen Emission Reduction

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Jixiang Zhang ◽  
Xuan Xi
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Bounded Rationality ◽  
Control Method ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Stable Region ◽  
Nitrogen Emissions ◽  
Nash Equilibrium Point ◽  
The Stability

In this paper, a decision-making competition game model concerning governments, agricultural enterprises, and the public, all of which participate in the reduction of nitrogen emissions in the watersheds, is established based on bounded rationality. First, the stability conditions of the equilibrium points in the system are discussed, and the stable region of the Nash equilibrium is determined. Then, the bifurcation diagram, maximal Lyapunov exponent, strange attractor, and sensitive dependence on the initial conditions are shown through numerical simulations. The research shows that the adjustment speed of three players’ decisions may alter the stability of the Nash equilibrium point and lead to chaos in the system. Among these decisions, a government’s decision has the largest effect on the system. In addition, we find that some parameters will affect the stability of the system; when the parameters become beneficial for enterprises to reduce nitrogen emissions, the increase in the parameters can help control the chaotic market. Finally, the delay feedback control method is used to successfully control the chaos in the system and stabilize it at the Nash equilibrium point. The research of this paper is of great significance to the environmental governance decisions and nitrogen reduction management.

scholarly journals A Dynamic Price Game Model in a Low-Carbon, Closed-Loop Supply Chain Considering Return Rates and Fairness Concern Behaviors

2019 ◽  
Vol 16 (11) ◽  
pp. 1978 ◽  
Author(s):  
Qiuxiang Li ◽  
Mengnan Shi ◽  
Yimin Huang
Keyword(s):  
Supply Chain ◽  
Price Adjustment ◽  
Stable Region ◽  
Game Model ◽  
Low Carbon ◽  
Return Rates ◽  
Dynamic Price ◽  
Price Game ◽  
Fairness Concern ◽  
Parameter Values

In this paper, we developed a dynamic price game model for a low-carbon, closed-loop supply chain system in which (1) the manufacturer had fairness concern and carbon emission reduction (CER) behaviors, and market share and profit maximization were their objectives, and (2) the retailer showed fairness concern behaviors in market competition and provided service input to reduce return rates. The retailer recycled old products from customers, and the manufacturer remanufactured the recycled old products. The effects of different parameter values on the stability and utility of the dynamic price game model were determined through analysis and numerical simulation. Results found that an increasing customer loyalty to the direct marketing channel decreased the stable region of the manufacturer’s price adjustment and increase that of the retailer. The stable region of the system shrank with an increase of CER and the retailer’s service level, which expanded with return rates. The dynamic system entered into chaos through flip bifurcation with the increase of price adjustment speed. In the chaotic state, the average utilities of the manufacturer and retailer all declined, while that of the retailer declined even more. Changes to parameter values had a great impact on the utilities of the manufacturer and retailer. By selecting appropriate control parameters, the dynamic system can return to a stable state from chaos again. The research of this paper is of great significance to participants’ price decision-making and supply chain operation management.

scholarly journals Dynamic Analysis and Chaos Control of Bertrand Triopoly Based on Differentiated Products and Heterogeneous Expectations

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Liuwei Zhao
Keyword(s):  
Dynamical System ◽  
Numerical Analysis ◽  
Equilibrium Point ◽  
Economic System ◽  
Dynamic Behavior ◽  
Game Model ◽  
Complex Dynamic ◽  
Heterogeneous Expectations ◽  
Price Game ◽  
The Stability

Price competition has become a universal commercial phenomenon nowadays. This paper considers a dynamic Bertrand price game model, in which enterprises have heterogeneous expectations. By the stability theory of the dynamic behavior of the Bertrand price game model, the instability of the boundary equilibrium point and the stability condition of the internal equilibrium point are obtained. Furthermore, bifurcation diagram, basin of attraction, and critical curve are introduced to investigate the dynamic behavior of this game. Numerical analysis shows that the change of model parameters in a dynamic system has a significant impact on the stability of the system and can even lead to complex dynamic behaviors in the evolution of the entire economic system. This kind of complex dynamic behavior will cause certain damage to the stability of the whole economic system, causing the market to fall into a chaotic state, which is manifested as a kind of market disorder competition, which is very unfavorable to the stability of the economic system. Therefore, the chaotic behavior of the dynamical system is controlled by time-delay feedback control and the numerical analysis shows that the effective control of the dynamical system can be unstable behavior and the rapid recovery of the market can be stable and orderly.

scholarly journals Computation of the Stability and Complexity about Triopoly Price Game Model with Delay Decision

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yuling Wang ◽  
Shubing Guo ◽  
Shide Duan
Keyword(s):  
Chaos Theory ◽  
Resource Constraints ◽  
Game Model ◽  
Entropy Theory ◽  
Yield Increase ◽  
Bifurcation Stability ◽  
Price Game ◽  
The Stability ◽  
The Cost ◽  
Delay Decision

We develop the price game model based on the entropy theory and chaos theory, considering the three enterprises are bounded rationality and using the cost function under the resource constraints; that is, the yield increase will bring increased costs. The enterprises of new model adopt the delay decision with the delay parameters τ1 and τ2, respectively. According to the change of delay parameters τ1 and τ2, the bifurcation, stability, and chaos of the system are discussed, and the change of entropy when the system is far away from equilibrium is considered. Prices and profits are found to lose stability and the evolution of the system tends to the equilibrium state of maximum entropy. And it has a big fluctuation with the increase of τ1 and τ2. In the end, the chaos is controlled effectively. The entropy of the system decreases, and the interior reverts to order. The results of this study are of great significance for avoiding the chaos when the enterprises make price decisions.

scholarly journals Research on the Complexity of Game Model about Recovery Pricing in Reverse Supply Chain considering Fairness Concerns

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Ting Li ◽  
Dongyun Yan ◽  
Shuxia Sui
Keyword(s):  
Supply Chain ◽  
Attraction Domain ◽  
Game Model ◽  
Maximum Lyapunov Exponent ◽  
Reverse Supply Chain ◽  
Nash Equilibrium Point ◽  
Price Game ◽  
Fairness Concerns ◽  
Attractor Bifurcation ◽  
Stable Area

A reverse recycling supply chain consisting of two recyclers is established in this paper, which takes into account the fact that the recyclers will consider the issue of fair concern in pricing. The paper discusses the local stability of the Nash equilibrium point in this price game model showing that the fair concern factors will reduce the stable area of the system. The paper also discusses the impacts of the sensitivity of the recovery price and the price cross coefficient on the stable area of the system. Through the method of system simulation and use of some indicators, such as the singular attractor, bifurcation diagram, attraction domain, power spectrum, and maximum Lyapunov exponent, the characteristics of the system at different times will be illustrated.

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