Complex dynamical behavior and numerical simulation of a Cournot-Bertrand duopoly game with heterogeneous players

Zhu, Yan-lan; Zhou, Wei; Chu, Tong; Elsadany, A. A.

doi:10.1016/j.cnsns.2021.105898

Cited by 13 publications

(3 citation statements)

References 43 publications

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“…Baiardi and Naimzada [4] studied the local stability and Neimark-Sacker bifurcations of an oligopoly model. Zhu et al [5] carried out a theoretical analysis on stability, coexistence of attractors, and contact bifurcation for a Cournot-Bertrand duopoly game model involving heterogeneous players. Askar and Al-khedhairi [6] implemented concrete discussion on local and global stability of the equilibrium points for a duopoly game concerning price competition.…”

Section: Introductionmentioning

confidence: 99%

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies.

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Section: Introductionmentioning

confidence: 99%

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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“…The system is solved numerically by finite difference methods. Numerical methods were also used for simulating the dynamical behavior of Cournot/Bertrand games and for further bifurcation analysis [47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

Stoykov

Kostov

2023

Games

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A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.

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“…Asker [5] explored the complex features of a Cournot-Bertrand game model with asymmetric market information. Zhu et al [48] considered a Cournot-Bertrand duopoly model which is characterized by different objective functions. The dynamical behaviors of the game are investigated by the stability region, bifurcation diagram, strange attractors and basin of attraction, etc.…”

mentioning

confidence: 99%

Complex dynamics of Cournot-Bertrand duopoly game with peer-induced fairness and delay decision

Zhang

Wang

2023

DCDS-B

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<p style='text-indent:20px;'>This paper establishes the Cournot-Bertrand duopoly game models with bounded rationality expectations under the assumption that the players are fair-minded agents who may adopt the delay decision. The existence and local stability of the equilibrium points are investigated. The effects of key parameters on the long-term dynamical evolution process of the models are investigated by numerical simulation. Furthermore, the performance of the players is examined using average profit and utility indexes. The results reveal that the excessively fast adjustment speeds and the higher fairness concern coefficients have a strong destabilizing impact on the system's stability. The product differentiation degree and delay strategy may be strong stabilizing or destabilizing factors for the game, which indicates that an appropriate product differentiation degree or delay weight is conducive to the system preserving its stability. In addition, when the system falls into periodic cycles or chaotic motions, the change trends of the players' performance may elevate or decline depending on the specific parameter conditions. Therefore, the chaos does not always necessarily detrimental to all the players in the Cournot-Bertrand duopoly game.</p>

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Complex dynamical behavior and numerical simulation of a Cournot-Bertrand duopoly game with heterogeneous players

Cited by 13 publications

References 43 publications

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

Complex dynamics of Cournot-Bertrand duopoly game with peer-induced fairness and delay decision

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