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The dynamics of a quantum Bertrand duopoly with differentiated products and heterogeneous expectations

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  • Zhang, Xinli
  • Sun, Deshan
  • Ma, Sijia
  • Zhang, Shuning

Abstract

Based on the bounded rationality and naïve expectation, the paper sets up a dynamic model of quantum Bertrand duopoly game with differentiated products by applying quantum game theory. We analyze the effect of quantum entanglement on stability of the quantum equilibrium points and complex dynamic behaviors. The result shows that the quantum entanglement can enhance the stability of the system. The adjustment speeds of bounded rational player can lead to chaotic characteristics of the system, the quantum entanglement can control the system’s chaos. Numerical simulations demonstrate the chaotic features via bifurcation, largest Lyapunov exponent, strange attractors, fractal dimensions and sensitivity to initial conditions.

Suggested Citation

  • Zhang, Xinli & Sun, Deshan & Ma, Sijia & Zhang, Shuning, 2020. "The dynamics of a quantum Bertrand duopoly with differentiated products and heterogeneous expectations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    • Handle: RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304544
    DOI: 10.1016/j.physa.2020.124878
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    References listed on IDEAS

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    Cited by:

    1. Grau-Climent, Juan & Garcia-Perez, Luis & Alonso-Sanz, Ramon & Losada, Juan C., 2023. "Effect of players’ expectations and memory in a quantum Cournot game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Zhou, Die & Pi, Jinxiu & Yang, Guanghui & Yang, Hui, 2022. "Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

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