Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control
Joint Authors
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-06-06
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Askar, S. S.& Al-khedhairi, A.. 2017. Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1151212
Modern Language Association (MLA)
Askar, S. S.& Al-khedhairi, A.. Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1151212
American Medical Association (AMA)
Askar, S. S.& Al-khedhairi, A.. Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1151212
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151212