Complexity Analysis of a Cournot-Bertrand Duopoly Game Model with Limited Information

Wang, Hongwu; Ma, Junhai

doi:10.1155/2013/287371

Cited by 31 publications

(36 citation statements)

References 18 publications

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“…In Cournot models, the way that firms control their production levels has a critical effect on market outputs. Conversely, in Bertrand models, firms select prices to be their strategic variables to optimize their profits [1,2]. Practically, the dynamic of an oligopoly game is complex, since each oligopolistic firm must consider both the consumers' behaviors and the reactions of all competitors [3].…”

Section: Introductionmentioning

confidence: 99%

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

2018

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This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm's preference is represented by a utility function that is derived from a constant elasticity of substitution (CES) production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations.

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Section: Introductionmentioning

confidence: 99%

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

2018

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“…The lead time can be reduced with an added cash cost and a service level constraint was also included in the research. Wang and Ma [11] centered on the limited information in a Cournot-Bertrand mixed duopoly game model. The bounded rational principles were used to help the two firms make management decisions.…”

Section: Introductionmentioning

confidence: 99%

Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

Ma¹,

Di²,

Ren³

2017

Complexity

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Apart from the price fluctuation, the retailers' service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer's service level which influences the market demand decided by customers' preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

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“…Ma and Pu [18] researched the complex characteristics on a Cournot-Bertrand duopoly model with heterogeneous goods, and the chaos control of the system was used by the state feedback method and the parameter variation control method. Wang and Ma [19] analyzed the complexity on a Cournot-Bertrand duopoly game model with limited information and discussed the influences of the parameters on the system features from the view of economics.…”

Section: Introductionmentioning

confidence: 99%

Research on a Dynamic Master-Slave Cournot Triopoly Game Model with Bounded Rational Rule and Its Control

Wang

2016

Mathematical Problems in Engineering

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The oligopoly market is modelled by a new dynamic master-slave Cournot triopoly game model with bounded rational rule. The local stabile conditions and the stable region are got by the dynamical systems bifurcation theory. The dynamics characteristics of the system with the changes of the adjustment speed parameters are analyzed by means of bifurcation diagram, largest Lyapunov exponents, phase portrait, and sensitive dependence on initial conditions. Furthermore, the parameters adjustment method is used to control the complex dynamical behaviors of the systems. The derived results have some important theoretical and practical meanings for the oligopoly market.

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Complexity Analysis of a Cournot-Bertrand Duopoly Game Model with Limited Information

Cited by 31 publications

References 18 publications

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

Research on a Dynamic Master-Slave Cournot Triopoly Game Model with Bounded Rational Rule and Its Control

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