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Nonlinear oligopolistic game with isoelastic demand function: Rationality and local monopolistic approximation

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  • Askar, S.S.
  • Alnowibet, K.

Abstract

Isoelastic demand function have been used in literature to study the dynamic features of systems constructed based on economic market structure. In this paper, we adopt the so-called Cobb–Douglas production function and study its impact on the steady state of an oligopolistic game that consists of four oligopolistic competitors or firms. Briefly, the paper handles three different scenarios. The first scenario introduces four oligopolistic firms who plays rational against each other in market. The firms use the myopic mechanism (or bounded rational) to update their production in the next time unit. The steady state of the obtained system in this scenario, which is the Nash equilibrium, is unique and its characteristics are investigated. Based on a local monopolistic approximation (LMA) strategy, one competitor prefers to play against the three rational firms and this is illustrated in the second scenario. The last scenario discusses the case when three competitors use the LMA strategy against a rational one. For all scenarios discrete dynamical systems are used to describe the game introduced in all scenarios. The stability analysis of the Nash equilibrium is investigated analytically and some numerical simulations are used to confirm the obtained analytical results.

Suggested Citation

  • Askar, S.S. & Alnowibet, K., 2016. "Nonlinear oligopolistic game with isoelastic demand function: Rationality and local monopolistic approximation," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 15-22.
    • Handle: RePEc:eee:chsofr:v:84:y:2016:i:c:p:15-22
    DOI: 10.1016/j.chaos.2015.12.019
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    3. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
    4. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    5. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Ren, Jing & Sun, Hao & Xu, Genjiu & Hou, Dongshuang, 2020. "Prediction on the competitive outcome of an enterprise under the adjustment mechanism," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    8. S. S. Askar, 2020. "Duopolistic Stackelberg game: investigation of complex dynamics and chaos control," Operational Research, Springer, vol. 20(3), pages 1685-1699, September.
    9. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.

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