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.

scholarly journals Equilibrium Further Studied for Combined System of Cournot and Bertrand: A Differential Approach

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bingyuan Gao ◽  
Yueping Du
Keyword(s):  
General Equilibrium ◽  
Equilibrium Point ◽  
Price Competition ◽  
Dynamic Equilibrium ◽  
Equilibrium Points ◽  
Cournot Model ◽  
Combined System ◽  
Quantity Competition ◽  
Bertrand Model ◽  
The Stability

In general, quantity competition and price competition exist simultaneously in a dynamic economy system. Whether it is quantity competition or price competition, when there are more than three companies in one market, the equilibrium points will become chaotic and are very difficult to be derived. This paper considers generally dynamic equilibrium points of combination of the Bertrand model and Cournot model. We analyze general equilibrium points of the Bertrand model and Cournot model, respectively. A general equilibrium point of the combination of the Cournot model and Bertrand model is further investigated in two cases. The theory of spatial agglomeration and intermediate value theorem are introduced. In addition, the stability of equilibrium points is further illustrated on celestial bodies motion. The results show that at least a general equilibrium point exists in combination of Cournot and Bertrand. Numerical simulations are given to support the research results.

scholarly journals Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Zhou ◽  
Na Zhao ◽  
Tong Chu ◽  
Ying-Xiang Chang
Keyword(s):  
Joint Venture ◽  
Fractal Structure ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Basins Of Attraction ◽  
Mixed Duopoly ◽  
Formation Mechanisms ◽  
Multiple Attractors ◽  
Homogeneous Product ◽  
The Stability

In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.

Simulation and Control of a Duopoly Model

2014 ◽  
Vol 472 ◽  
pp. 146-151
Author(s):  
Ya Li Lu
Keyword(s):  
Nash Equilibrium ◽  
Demand Function ◽  
Delayed Feedback Control ◽  
Control Scheme ◽  
Duopoly Model ◽  
Adjustment Speed ◽  
The Stability ◽  
Boundary Fixed Points ◽  
And Control ◽  
Time Delayed Feedback

This paper studies the dynamics of a duopoly model with bounded rationality and nonlinear demand function. Based on the stability theorem and Jurys criterions, we prove that the model has two unstable boundary fixed points and a local stable Nash equilibrium. Then we depict the stability region of Nash equilibrium, and investigate the effects of output adjustment speed on the players profit respectively. Theoretical analysis and simulations show that higher output adjustment speed can result in chaotic variation of outputs, and that the Nash equilibrium is the optimal result of duopoly game. To improve the profitability of each player and achieve the optimal game result, we put forth a new scheme combined with the time-delayed feedback control and the limiter control to stabilize the output to Nash equilibrium. Finally, the numerical simulation is adopted to verify the effectiveness and feasibility of the above control scheme.

Theoretical and practical aspects of analysis of competitiveness of insurance company

10.12737/585 ◽  
2013 ◽  
Vol 1 (2) ◽  
pp. 25-30 ◽  
Author(s):  
Медушевская ◽  
Inna Medushevskaya
Keyword(s):  
Price Competition ◽  
Swot Analysis ◽  
Insurance Market ◽  
Financial Ratios ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Group ◽  
Determining Factors

In the article the theoretical and practical aspects of the analysis of the competitiveness of the insurance company CJSC «Insurance Group Uralsib» as an example were revieled. The competitiveness of the insurance companies is based on the general principles and provisions of the theory of competition and competitiveness. It was detailed the concept of competition in the insurance market, revealed its specificity and the possible non-price competition on it. The competitiveness of the insurance company is considered as a multi-faceted category, its determining factors were reflected. The competitiveness of Penza branch based on the analysis of financial ratios was evaluated and conducted the SWOT-analysis. The recommendations were given.

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 Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 257 ◽  
Author(s):  
B. A. Pansera ◽  
L. Guerrini ◽  
M. Ferrara ◽  
T. Ciano
Keyword(s):  
Continuous Time ◽  
Delay Differential Equations ◽  
Price Competition ◽  
Time Delays ◽  
Equilibrium Points ◽  
Hopf Bifurcations ◽  
Stage Game ◽  
Set Up ◽  
The Stability ◽  
Delay Differential

The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.

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 Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
LiuWei Zhao
Keyword(s):  
Demand Function ◽  
Complex Dynamics ◽  
Delayed Feedback Control ◽  
Flip Bifurcation ◽  
Bifurcation And Chaos ◽  
Stability And Instability ◽  
The Stability ◽  
And Control ◽  
Time Delayed Feedback ◽  
Dynamic Phenomena

A dynamic multimarket Cournot model is introduced based on a specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is carried out on the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can lose stability via flip bifurcation or Neimark-Sacker bifurcation and time-delayed feedback control is used to stabilize the chaotic behaviors of the system.

scholarly journals Complex Dynamics of Mixed Triopoly Game with Quantity and Price Competition

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jing Wang ◽  
Zhenhua Bao ◽  
Junqing Huang ◽  
Yujing Song
Keyword(s):  
Nash Equilibrium ◽  
Price Competition ◽  
Control Method ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Private Firms ◽  
Public Firm ◽  
Feedback Control Method

This article investigates the dynamics of a mixed triopoly game in which a state-owned public firm competes against two private firms. In this game, the public firm and private firms are considered to be boundedly rational and naive, respectively. Based on both quantity and price competition, the game’s equilibrium points are calculated, and then the local stability of boundary points and the Nash equilibrium points is analyzed. Numerical simulations are presented to display the dynamic behaviors including bifurcation diagrams, maximal Lyapunov exponent, and sensitive dependence on initial conditions. The chaotic behavior of the two models has been stabilized on the Nash equilibrium point by using the delay feedback control method. The thresholds under price and quantity competition are also compared.

scholarly journals On the Stability and Multistability in a Duopoly Game with R&D Spillover and Price Competition

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Wei Zhou ◽  
Xiao-Xue Wang
Keyword(s):  
Price Competition ◽  
Equilibrium Points ◽  
Research Result ◽  
Basin Of Attraction ◽  
Profit Maximization ◽  
Feasible Region ◽  
Multiple Attractors ◽  
Critical Curves ◽  
Coexistence Of Multiple Attractors ◽  
The Stability

In this paper, a dynamical two-stage game with R&D competition and joint profit maximization is built. The stability of all the equilibrium points is discussed through Jury condition, and the stability region of the Nash equilibrium point is then given. The influence of the parameters on the system is discussed, and we find that the firm can even benefit from chaos, when it has higher innovation efficiency and higher adjusting speed. And then the coexistence of multiple attractors is studied using basin of attraction. Our research result shows that the coexisting attractors can be observed in the two-parameter bifurcation diagram. At last, the boundary of feasible region, global bifurcations, and formation mechanism of fractal structure of attracting basin are analyzed through critical curves and noninvertible map theory.

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