On Puu’s incomplete information formulation for the standard and multi-team Bertrand game

Ahmed, E.; Elettreby, M. F.; Hegazi, A. S.

doi:10.1016/j.chaos.2005.08.198

Cited by 19 publications

(16 citation statements)

References 9 publications

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“…They assumed the existence of two identical competitors in the model, studied the mapping symmetry of this model, and found complex dynamic behaviors in the model. With study on the nonlinear cost and introduction of the bounded rational expectation, Ahmed et al [21,22] improved the demand function on the basis of which the duopoly game model was to be established and then the duopoly model would be extended to the multidimensional model. It could be concluded that when the game party makes adjustments to the market too fast, the system would present the complex phenomena such as bifurcation and chaos.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Yan

2019

Complexity

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With application of nonlinear theory, this paper makes study on the long-term competition in a recycling price game model by manufacturers and retailers. The paper makes analysis on the local stability of the Nash equilibrium point and gives the corresponding stable region. It has been found that the stability of the whole system would be significantly impacted by the following factors which include adjustment speed of the recycling price, the proportion of recycled products by channels, the sensitivity of consumers for the recycling price, and the price cross-elasticity between two channels. By means of the simulation technology, the complexity of the recycling price in the system in the long-term competition has been demonstrated. Owing to the change of parameters, bifurcation, chaos, and other phenomena would appear in the system. When the system is becoming chaotic, the profit of the whole system decreased. All these show that the operational efficiency for the whole system will be impaired by the chaos. Effective chaotic control of the system will be realized by the use of the parameter adaptation method.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Yan

2019

Complexity

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“…unstable) ∀α <α q (resp. ∀α >α l ); if α ∈ (α q ,α l ) then E * q is locally unstable while E * l is locally stable; (ii) if a < 1 2 then E * q and E * l are both locally stable (resp. unstable) ∀α <α l (resp.…”

Section: Independent Productsmentioning

confidence: 99%

“…Indeed, some exceptions actually exist in this direction. Specifically, Ahmed et al [1] have taken into account a multi-team Bertrand game where the dynamics of the economy is studied by considering the "Puu's incomplete information dynamical system" [1], p. 1182, that followed the work of Puu [15]. Subsequently, Zhang et al [17] have studied the local properties of a repeated duopoly model with price competition, linear demand, linear costs and incomplete information of players, while Fanti et al [11] have revisited their work by pointing out microeconomic foundations and the global analysis.…”

Section: Introductionmentioning

confidence: 98%

Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences

Brianzoni

Gori

Michetti

2015

Chaos, Solitons & Fractals

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a r t i c l e i n f o Article history: Available online xxx a b s t r a c tThis paper studies mathematical properties and dynamics of a duopoly with price competition and horizontal product differentiation by introducing quadratic production costs (decreasing returns to scale), thus extending the model with linear costs (constant returns to scale) of Fanti et al. [11]. The economy is described by a two-dimensional non-invertible discrete time dynamic system. The paper first determines fixed points and other invariant sets, showing that synchronized dynamics can occur. Then, stability properties are compared in the cases of quadratic costs and linear costs by considering the degree of product differentiation and the speed of adjustment of prices as key parameters. It is also shown that synchronization takes place if products tend to be relatively complements and stressed similarities and differences between models with quadratic and linear costs. Finally, the paper focuses on the phenomenon of multistability thus underlying new evidences in comparison with the model with linear costs.

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“…Most of the recent literature deals with simplified versions of the Puu model (8), cf. [8][9][10][11], and none of them analyzes the dynamic behavior of the Puu model in detail. Naimzada and Ricchiuti [10] propose to use a demand function (1) without inflection point to achieve a onedimensional map.…”

Section: Introductionmentioning

confidence: 99%

On periodic and chaotic behavior in a two-dimensional monopoly model

Al-Hdaibat

Govaerts

Neirynck

2015

Chaos, Solitons & Fractals

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On Puu’s incomplete information formulation for the standard and multi-team Bertrand game

Cited by 19 publications

References 9 publications

Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences

On periodic and chaotic behavior in a two-dimensional monopoly model

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