Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion

Xin, Baogui; Wang, Yanying

doi:10.1109/access.2020.2976501

Cited by 6 publications

(4 citation statements)

References 33 publications

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“…It is known that stochastic perturbation is an important factor in the economy. For example, Xin and Wang [47] proposed a stochastic Cournot duopoly game in a block chain cloud services market driven by Brownian motion. However, there is still a lack of research on fractional Cournot oligopoly games with stochastic perturbation.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Ran,

Zhou

2024

Complexity

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A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

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Section: Introductionmentioning

confidence: 99%

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Ran,

Zhou

2024

Complexity

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“…Long‐term stable development to achieve win‐win economic and social benefits is also a particular concern of firms. Previous studies on the production adjustment of firms usually used an oligopoly game [17, 18]. Driskill et al [17] introduced a duopoly market and considered the loss generated during output adjustment.…”

Section: Introductionmentioning

confidence: 99%

Stability of a mean field game of production adjustment

Wang

Xin

2023

Asian Journal of Control

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We propose a mean field game model to study the stability of production adjustment by extending a kind of linear quadratic Gaussian game in large population systems. First, we present the model's equilibrium solutions by a backward HJB equation and a forward FPK equation. Second, we employ the local perturbation method to transform the nonlinear problem into a linear one to study the solutions' stability. Third, we use the spectrum and contraction analyses to study the stationary solutions' linear stability. At last, we validate the results by the numerical simulation. The results show that the additional cost coefficient and noise intensity affect the system's stability. If the additional cost coefficient and the noise intensity are large enough for firms to change their outputs, then firms will try to reduce their production adjustment and remain stable long‐term.

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“…Furthermore, in the Ref. [18][19][20][21], the factors of service level or service spillover effect were considered in the establishment of supply chain model. Unfortunately, few literatures use the knowledge of nonlinear dynamics and numerical simulation tools to study these dynamic game models.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamical behaviors in a Bertrand game with service factor and differentiated products

Zhou

2021

Nonlinear Dyn

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In this paper, taking the factor of service level provided by the manufacturers into consideration, a static duopolistic Bertrand game with service factor is studied first, in which these two oligarchs produce differentiated products. A dynamic game model of duopoly Bertrand with boundedly rational is established with using the gradient mechanism. By using numerical simulation tools, there are two paths for the system to drop into chaos, that is, flip bifurcation and Neimark-Sacker bifurcation. The symmetric structures can be found from two-parameter bifurcation diagrams. Saddle-homoclinic bifurcation also can be observed from the evolution process of phase portraits. In addition, the emergence of intermittent chaos implies that the established system has the capability of self-regulating, where PM-I intermittency, PM-III intermittency and crisis-induced intermittency have been studied. With the help of the critical curves, the qualitative changes on the basin of attraction are investigated. At last, it can be found that the values of product differentiation degree and service spillover effect are not the bigger the better. Keeping these two parameters in a relatively small range will be conducive to the long-term stable operation of the two manufacturers.

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Stability and Hopf Bifurcation of a Stochastic Cournot Duopoly Game in a Blockchain Cloud Services Market Driven by Brownian Motion

Cited by 6 publications

References 33 publications

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Stability of a mean field game of production adjustment

Complex dynamical behaviors in a Bertrand game with service factor and differentiated products

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