Dynamic Cournot oligopoly game based on general isoelastic demand

Andaluz, Joaquı́n; Elsadany, A. A.; Jarne, Gloria

doi:10.1007/s11071-019-05333-7

Cited by 22 publications

(21 citation statements)

References 23 publications

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“…A deep analysis of a class of oligopoly markets is presented in [1]. In section 2 in [1] authors analyze market equilibrium, obtained by the use of the first and second order conditions.…”

Section: Some Applications On Newly Investigated Oligopoly Modelsmentioning

confidence: 99%

“…A deep analysis of a class of oligopoly markets is presented in [1]. In section 2 in [1] authors analyze market equilibrium, obtained by the use of the first and second order conditions. They have assumed P (Q) = Q −1/η , where P be the market price, x, y ≥ 0 are the quantity supplied by firm one and two, respectively, Q = x + y be the total output and η > 0 be a parameter.…”

Section: Some Applications On Newly Investigated Oligopoly Modelsmentioning

confidence: 99%

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Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Kabaivanov¹,

Zhelinski²,

Zlatanov³

2021

Preprint

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In this paper we generalize Hardy-Rogers maps in the context of coupled fixed points. We generalizes with the help of the obtained main theorem some known results about existence and uniqueness of market equilibrium in duopoly markets. We investigate some recent results about market equilibrium in duopoly markets with the help of the main theorem and we enrich them. We define a generalized response function including production and surpluses. Finally we illustrate a possible application of the main result in the investigation of market equilibrium, when the pay off functions are non differentiable.

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“…A deep analysis of a class of oligopoly markets is presented in [1]. In section 2 in [1] authors analyze market equilibrium, obtained by the use of the first and second order conditions.…”

Section: Some Applications On Newly Investigated Oligopoly Modelsmentioning

confidence: 99%

Section: Some Applications On Newly Investigated Oligopoly Modelsmentioning

confidence: 99%

Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Kabaivanov¹,

Zhelinski²,

Zlatanov³

2021

Preprint

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“…Discrete oligopoly dynamics based on company profit maximizations have been considered [1][2][3][4][5][6][7]. Furthermore, these models have been utilized to examine the dynamic characteristics of competitive markets, which has been classified as steady state, periodic, and chaotic [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game

Al-khedhairi

Elsadany

Elsonbaty

2022

Mathematical Problems in Engineering

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A discreet fractional-order Cournot–Bertrand competition duopoly game is introduced based on the fractional-order difference calculus of the Caputo operator. The model is designed when players can make long memory decisions. The local stability of equilibrium points is discussed for the proposed model. Some numerical simulations explore the model’s bifurcation and chaos by employing bifurcation diagrams, phase portraits, maximal Lyapunov exponents, and time series. According to our findings, the fractional-order parameter has an effect on the game’s stability and dynamics.

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“…Most discrete time oligopoly dynamics that have been considered in the past two decades were based on the single objective of maximizing profit of firms [7][8][9][10]. More recently, the stable, periodic, and chaotic dynamic behaviors of these markets can be analyzed on the basis of these models [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

2021

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A Cournot duopoly game is a two-firm market where the aim is to maximize profits. It is rational for every company to maximize its profits with minimal sales constraints. As a consequence, a model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. The CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. The current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. In the event of sales constraint and no sales constraint, the local stability conditions of the Cournot equilibrium are derived. The initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Two routes to chaos are analyzed by numerical simulation using 2D bifurcation diagram, one of which is period doubling bifurcation and the other is Neimark–Sacker bifurcation. Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms.

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Dynamic Cournot oligopoly game based on general isoelastic demand

Cited by 22 publications

References 23 publications

Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game

Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

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