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

Askar, Sameh

doi:10.1155/2013/809795

Cited by 14 publications

(10 citation statements)

References 19 publications

(23 reference statements)

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“…Mostly, in the literature, we see developments of the Nash-Cournot equilibrium towards the resolution of other research questions, especially connected with the asymptotic stability of a variously associated dynamical system (see [1]).…”

Section: Bayesian Games In Industrial Organizationmentioning

confidence: 99%

Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Carfì

Donato

2018

Mathematics

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In this paper, we consider a Cournot duopoly, in which any firm does not know the marginal costs of production of the other player, as a Bayesian game. In our game, the marginal costs depend on two infinite continuous sets of states of the world. We shall study, before the general case, an intermediate case in which only one player, the second one, shows infinitely many types. Then, we shall generalize to the case in which both players show infinitely many types depending on the marginal costs, where the marginal costs are given by the nature and each actual marginal cost is known only by the respective player. We find, in both cases, the general Nash equilibrium.

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Section: Bayesian Games In Industrial Organizationmentioning

confidence: 99%

Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Carfì

Donato

2018

Mathematics

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“…Using a demand function with no inflection points, complex behaviors such as bifurcation and chaos have been investigated in [4]. Askar [5] has shown some important results about Cournot duopoly game that was formed by a concave demand function. Other investigations on those complex characteristics can be found in [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Askar

Al-khedhairi

2017

Discrete Dynamics in Nature and Society

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Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu's mechanism to update their productions. Puu's mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

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“…Chaotic economic systems such as monopoly and duopoly are sophisticated systems on which the chaos that occurs in them is more difficult than those found in Lorenz, logistic, and Rössler. In [22], the author has introduced a new Cournot duopoly model on which an unknown demand function without inflection points has been studied. This model has shown complex dynamical properties such as hard bifurcation and bad chaos.…”

Section: Introductionmentioning

confidence: 99%

Image Encryption Algorithm Based on Chaotic Economic Model

Askar

Karawia

Alshamrani

2015

Mathematical Problems in Engineering

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In literature, chaotic economic systems have got much attention because of their complex dynamic behaviors such as bifurcation and chaos. Recently, a few researches on the usage of these systems in cryptographic algorithms have been conducted. In this paper, a new image encryption algorithm based on a chaotic economic map is proposed. An implementation of the proposed algorithm on a plain image based on the chaotic map is performed. The obtained results show that the proposed algorithm can successfully encrypt and decrypt the images with the same security keys. The security analysis is encouraging and shows that the encrypted images have good information entropy and very low correlation coefficients and the distribution of the gray values of the encrypted image has random-like behavior.

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

Cited by 14 publications

References 19 publications

Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Image Encryption Algorithm Based on Chaotic Economic Model

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