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 Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Hongliang Tu ◽  
Xueli Zhan ◽  
Xiaobing Mao
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Complex Dynamics ◽  
Spillover Effects ◽  
Game Model ◽  
Complex Dynamic ◽  
Nash Equilibrium Point ◽  
Straight Line ◽  
Stable Conditions ◽  
The Stability

We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.

scholarly journals Research on the Complex Dynamic Characteristics and RLS Estimation’s Influence Based on Price and Service Game

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Zhanbing Guo
Keyword(s):  
Least Squares ◽  
Fixed Points ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Recursive Least Squares ◽  
Game Model ◽  
Complex Dynamic ◽  
Service Market ◽  
The Real ◽  
Price Game

Considering that the real competitions in service market contain two important factors, price and service, we build a dynamical price and service game model and study the complex dynamics of this bivariate game. Some special properties about the adjustment of service are noted by comparing our innovative bivariate game model with previous univariate game model. Besides, we discuss the stabilities of fixed points and compare the price and service game with price game. What is more, the recursive least-squares (RLS) estimation is introduced to substitute naive estimation; then the impacts of RLS estimation are studied by comparing it with naive estimation.

Simulation and Analysis of Dynamic Evolution of Electricity Market Based on Bidding Decisions with Heterogeneous Expectations

2010 ◽  
Vol 37-38 ◽  
pp. 1153-1156
Author(s):  
Meng Zhang ◽  
Hong Ming Yang ◽  
De Lun Yang
Keyword(s):  
Nash Equilibrium ◽  
Electricity Market ◽  
Power Network ◽  
Complex Dynamic ◽  
Heterogeneous Expectations ◽  
Dynamic Behaviors ◽  
Market Participants ◽  
Complementarity Function ◽  
Nonlinear Complementarity Function ◽  
The Stability

Based on different bidding decisions with heterogeneous expectations of market participants, a dynamic model of electricity market considering power network constraints is proposed. This model is represented by a discrete difference equations embedded with the optimization problem of market clearing. By using the nonlinear complementarity function, the complex dynamic behaviors of electricity market are simulated and analyzed. The Nash equilibrium and its stability, the periodic and even chaotic dynamic behaviors beyond the stability region of Nash equilibrium are investigated.

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.

PROBABILISTIC DETERMINATION OF STABILITY FOR A DELAY-DIFFERENTIAL MODEL OF THE GLUCOSE-INSULIN DYNAMICAL SYSTEM

1999 ◽  
Vol 07 (02) ◽  
pp. 131-144 ◽  
Author(s):  
A. DE GAETANO ◽  
O. ARINO
Keyword(s):  
Dynamical System ◽  
Equilibrium Point ◽  
Stability Criterion ◽  
Model Parameters ◽  
Qualitative Behavior ◽  
System Modelling ◽  
Differential Model ◽  
The Stability ◽  
Delay Differential

Some of the questions involved in the formulation of a new model for a physiological phenomenon, when the model represents a dynamical system, concern its qualitative behavior. The determination of the stability of a particular dynamical system is usually made analytically, from a linearization of the system around an equilibrium point. This analytic proof may often be complicated or impossible, leading to the imposition of conditions on the relative magnitude of the model structural parameters or to other partial results. We discuss a general technique whereby a probabilistic judgement is made on the stability of a dynamical system, and we apply it to the study of a particular delay differential system modelling the relationship between insulin secretion and glucose uptake. This technique is applicable in case experimental material is available: a stability criterion is obtained via the usual linearization around an equilibrium point and its distribution is approximated from the estimated dispersion of the model parameters. The probability that the stability criterion is such as to make the model stable can then be computed directly. While the conclusion is probabilistic in nature, it is generally applicable to a vast class of models.

Spatiotemporal Dynamics of Phytoplankton-Fish System with the Allee Effect and Harvest Effect

2013 ◽  
Vol 726-731 ◽  
pp. 1604-1610
Author(s):  
Wei Wei Zhang ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Pattern Formation ◽  
Equilibrium Point ◽  
Allee Effect ◽  
Spatiotemporal Dynamics ◽  
The Stability ◽  
Fish Interactions

In this paper, spatiotemporal dynamics of a phytoplankton-fish system with the Allee effect and harvest effect are investigated mathematically and numerically. Mathematical theoretical works have been pursued for the investigation of the stability of the equilibrium point of the phytoplankton-fish system with the Allee effect and harvest effect, which in turn provide a theoretical basic for the numerical simulation. Numerical analysis works indicate that Allee effect and harvest effect have a strong effect on the spatiotemporal dynamics of the phytoplankton-fish system using pattern formation. These results may help us to better understand phytoplankton-fish interactions.

Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

2016 ◽  
Vol 26 (11) ◽  
pp. 1650183 ◽  
Author(s):  
Feng Liu ◽  
Yaguang Li
Keyword(s):  
Control Method ◽  
Discrete Dynamical System ◽  
Nonlinear Dynamic System ◽  
Economic Systems ◽  
Complex Dynamic ◽  
Heterogeneous Players ◽  
Price Game ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
The Stability

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

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.

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