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A discrete fractional-order Cournot duopoly game

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  • Xin, Baogui
  • Peng, Wei
  • Kwon, Yekyung

Abstract

This paper focuses on associating the Cournot duopoly problem with long-memory effects. First of all, we generate a discrete fractional-order Cournot duopoly game by introducing the Caputo fractional-order difference calculus to the classical duopoly theory. In the fractional-order game, participants can make their decisions by taking full advantage of their historical information. Then we discuss both Nash equilibria and local stability of the game by employing the linear approximation theory. At last, we numerically validate the main results by using bifurcation diagrams, phase portraits, the largest Lyapunov exponent, and the 0–1 test algorithms.

Suggested Citation

  • Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305185
    DOI: 10.1016/j.physa.2020.124993
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    References listed on IDEAS

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    1. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    2. Baogui Xin & Junhai Ma & Qin Gao, 2008. "Complex Dynamics of an Adnascent-Type Game Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
    3. Li, Tingting & Xie, Jinxing & Lu, Shengmin & Tang, Jiafu, 2016. "Duopoly game of callable products in airline revenue management," European Journal of Operational Research, Elsevier, vol. 254(3), pages 925-934.
    4. Hashemi, M.S. & Inc, Mustafa & Yusuf, Abdullahi, 2020. "On three-dimensional variable order time fractional chaotic system with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2019. "An oligopoly model with rational and imitation rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 254-278.
    6. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    7. Xinhua Wang & Rongwu Lu & Hao Yu & Dan Li, 2019. "Stability of the Evolutionary Game System and Control Strategies of Behavior Instability in Coal Mine Safety Management," Complexity, Hindawi, vol. 2019, pages 1-14, February.
    8. Askar, S.S. & Alshamrani, Ahmad M. & Alnowibet, K., 2016. "The arising of cooperation in Cournot duopoly games," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 535-542.
    9. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    10. Rongwu Lu & Xinhua Wang & Hao Yu & Dan Li, 2018. "Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application," Complexity, Hindawi, vol. 2018, pages 1-10, March.
    11. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    12. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    13. Agliari, A. & Naimzada, A.K. & Pecora, N., 2016. "Nonlinear dynamics of a Cournot duopoly game with differentiated products," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 1-15.
    14. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    15. A. Matsumoto, 2006. "Controlling the Cournot-Nash Chaos," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 379-392, February.
    16. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    17. Akinlar, Mehmet Ali & Tchier, Fairouz & Inc, Mustafa, 2020. "Chaos control and solutions of fractional-order Malkus waterwheel model," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
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