On Persistence in Multiobjective Oligopoly

Ahmed, E.; Hegazi, A. S.; El-Hafez, A.T. Abd

doi:10.1142/s0129183101002085

Cited by 3 publications

(5 citation statements)

References 3 publications

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“…It is known elsewhere [13,18] the significance of speed of adjustment ( ). It is a positive function which gives the extent of production variation of th firm following a given profit signal.…”

Section: Model and Main Resultsmentioning

confidence: 99%

“…To other people, risk must be quantified in terms of a surrogate for the overall cost, such as its mean value, median value, or worst possible value [12]. An alternative approach for risk measurement has been introduced in detail by Ahmed et al [13]. In [13], Ahmed et al have modeled risk in Cournot game based on multiobjective method.…”

Section: Introductionmentioning

confidence: 99%

“…An alternative approach for risk measurement has been introduced in detail by Ahmed et al [13]. In [13], Ahmed et al have modeled risk in Cournot game based on multiobjective method. Ahmed et al [13] have used the standard deviation for modeling risk in Cournot game.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], Ahmed et al have modeled risk in Cournot game based on multiobjective method. Ahmed et al [13] have used the standard deviation for modeling risk in Cournot game.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

Askar

2013

Journal of Applied Mathematics

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It is reported in the literature that the most fundamental idea to address uncertainty is to begin by condensing random variables. In this paper, we propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points. A random cost function is introduced in this model. Each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multiobjective optimization problem, the expectation and worst-case approaches are used. A model of two rational firms that are in competition and produce homogenous commodities is introduced using an unknown demand function. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation, and chaos are investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation.

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Section: Model and Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In [13], Ahmed et al have modeled risk in Cournot game based on multiobjective method. Ahmed et al [13] have used the standard deviation for modeling risk in Cournot game.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

Askar

2013

Journal of Applied Mathematics

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“…e earliest was by Kamerschen and Smith [19], who showed that the stability of their duopoly model depends on the production cost and the coefficients in the linear demand function. In their work, by including risk minimization into their profit maximization oligopoly model, Ahmed et al [20] showed that giving more weight to risk minimization decreases profit. In another work, Ahmed et al [21] showed that a multiobjective oligopoly model is more stable than a single objective one.…”

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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Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Askar

Al-khedhairi

2020

Mathematics

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The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

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On Persistence in Multiobjective Oligopoly

Cited by 3 publications

References 3 publications

The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

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

Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

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