Differentiated Cournot duopoly game with fractional-order and its discretization
ISSN: 0264-4401
Article publication date: 8 May 2019
Issue publication date: 8 May 2019
Abstract
Purpose
Fractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims to explore a proposed fractional-order differentiated Cournot duopoly game and its discretized game.
Design/methodology/approach
Conditions for existence and uniqueness of the proposed game’s solution are derived. The existence of Nash equilibrium point and its local and global stability are obtained. Furthermore, local stability analysis of the discretized game is investigated. The effects of fractional-order on game’s dynamics are examined, along with other parameters of the game, via the 2D bifurcation diagrams in planes of system’s parameters are acquired.
Findings
Theoretical and numerical simulation results demonstrate rich variety of interesting dynamical behaviors such as period-doubling and Neimark–Sacker bifurcations, attractors’ crises in addition to chaotic attractors. The results demonstrated that the stability Nash equilibrium point of the game can be lost by period doubling or Neimark–Sacker bifurcations.
Practical implications
Oligopoly games are pivotal in the mathematical modeling of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also macroeconomic analysis of business cycles, innovation and growth.
Originality/value
Although the Cournot game and its variants have attracted great interest among mathematicians and economists since the time of its proposition till present, memory effects in continuous-time and discrete-time Cournot duopoly game have not been addressed yet. To the best of author’s knowledge, this can be considered as the first attempt to investigate this problem of fractional-order differentiated Cournot duopoly game. In addition, studying more realistic models of Cournot oligopoly games plays a pivotal role in the mathematical investigation and better understanding of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also in macroeconomic analysis of business cycles, innovation and growth.
Keywords
Acknowledgements
The author would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this research (Group no. RG -1438-046).
The author would like to thank anonymous reviewers for their helpful comments and suggestions which greatly improve original manuscript of the paper.
Conflict of interest: The author declares that there is no conflict of interest regarding the publication of this paper.
Data Availability: The data used to support the findings of this study are included within the article.
Citation
Al-khedhairi, A. (2019), "Differentiated Cournot duopoly game with fractional-order and its discretization", Engineering Computations, Vol. 36 No. 3, pp. 781-806. https://doi.org/10.1108/EC-07-2018-0333
Publisher
:Emerald Publishing Limited
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