scholarly journals Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

2021 ◽  
pp. 47-57
Author(s):  
Yuqi Dou ◽  
Xingyu Liu
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Systems ◽  
Complex Dynamics ◽  
Rational Expectation ◽  
Profit Maximization ◽  
Mixed Duopoly ◽  
Complex Dynamic ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
Relative Profit

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

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.

Synergistic Approach to Enterprise Management

2015 ◽  
Vol 4 (3) ◽  
pp. 4-13
Author(s):  
Заковоротный ◽  
Vilor Zakovorotnyy ◽  
Угнич ◽  
Ekaterina Ugnich ◽  
Флек ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Dynamic Model ◽  
Dynamic Systems ◽  
Self Organization ◽  
Enterprise Management ◽  
Economic Systems ◽  
Complex Dynamic ◽  
Complex Dynamic Systems ◽  
Synergistic Approach ◽  
The Stability

The research reveals the peculiarities of synergistic model of enterprise management in market conditions. The possibilities of synergistic approach application towards the study of economic systems are shown in the article. On the basis of theoretical analysis of complex dynamic systems basic rules are identified which must be taken into consideration while examining the enterprise as a system in which the processes of self-organization exist. A generalized dynamic model of an enterprise in market environment is presented. It is carried out the analysis of the established condition of the enterprise as a system and the stability of its stationary state.

scholarly journals Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Junhai Ma ◽  
Hongwu Wang
Keyword(s):  
Mixed Model ◽  
Historical Data ◽  
Complex Dynamics ◽  
Dynamic Properties ◽  
Stable Region ◽  
Mixed Duopoly ◽  
Game Model ◽  
Complex Dynamic ◽  
Delayed System ◽  
Route To Chaos

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

On the Stability of Linear Discrete Dynamic Systems

1970 ◽  
Vol 37 (2) ◽  
pp. 271-275 ◽  
Author(s):  
J. A. Walker
Keyword(s):  
Dynamic Systems ◽  
Energy Method ◽  
Energy Function ◽  
Degrees Of Freedom ◽  
Symmetric Matrix ◽  
Discrete Dynamic ◽  
Stability Theorems ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
General Method

A technique is presented for studying the stability of equilibria of linear discrete dynamic systems involving general types of forces: elastic, nonconservative, dissipative, and gyroscopic. The techniqe is a generalization of the energy method, based upon a restricted version of the general method of Liapunov, and often allows stability to be determined in terms of unspecified parameters. For systems of n degrees of freedom, stability theorems are given which require the existence of an n × n symmetric matrix G having certain properties. Several examples are given to illustrate the method of construction of this matrix and the type of information which it may be expected to yield. In general the method and its results are quite similar to the energy method, but apply even when the energy function does not exist.

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 Complex Dynamic Systems View on Conceptual Change: How a Picture of Students’ Intuitive Conceptions Accrue From Dynamically Robust Task Dependent Learning Outcomes

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Ismo T. Koponen ◽  
Tommi Kokkonen ◽  
Maiji Nousiainen
Keyword(s):  
Conceptual Change ◽  
Learning Outcomes ◽  
Dynamic Systems ◽  
Computational Modelling ◽  
Complex Dynamic ◽  
Complex Dynamic Systems ◽  
Intuitive Conceptions ◽  
Context Dependent ◽  
The Stability ◽  
Dependent Learning

We discuss here conceptual change and the formation of robust learning outcomes from the viewpoint of complex dynamic systems (CDS). The CDS view considers students’ conceptions as context dependent and multifaceted structures which depend on the context of their application. In the CDS view the conceptual patterns (i.e. intuitive conceptions here) may be robust in a certain situation but are not formed, at least not as robust ones, in another situation. The stability is then thought to arise dynamically in a variety of ways and not so much to mirror rigid ontological categories or static intuitive conceptions. We use computational modelling to understand the generic dynamic and emergent features of that phenomenon. The model is highly simplified and idealized, but it shows how context dependence, described here by an epistemic landscape structure, leads to the formation of context dependent robust states that can be viewed as attractors in learning, and how owing to the sharply defined nature of these states, learning appears as a progression of switches from one state to another, giving thus the appearance of conceptual change as switches from one robust state to another. Finally, we discuss the implications of the results in directing attention to the design of learning tasks and their structure, and how empirically accessible learning outcomes might be related to these underlying factors.

scholarly journals Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Longfei Wei ◽  
Haiwei Wang ◽  
Jing Wang ◽  
Jialong Hou
Keyword(s):  
Nash Equilibrium ◽  
Price Competition ◽  
Equilibrium Points ◽  
Private Insurance ◽  
Insurance Market ◽  
Delayed Feedback Control ◽  
Mixed Duopoly ◽  
Flip Bifurcation ◽  
Insurance Company ◽  
The Stability

This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

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