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The influence of entanglement on complex dynamics of a quantum Stackelberg duopoly with heterogeneous expectations

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Abstract

This paper investigates the complex dynamics of a nonlinear discrete-time Stackelberg duopoly game model by applying quantum game theory, where the players have heterogeneous expectations: the leader is boundedly rational and the follower thinks with adaptive expectation. The local stability of quantum equilibrium, the influence of quantum entanglement on stability region and complex dynamic behavior of the system are analyzed. The result shows that the stability of quantum Nash equilibrium can increase with the quantum entanglement increasing. The complex chaotic behaviors can appear when the quantum quantity adjustment speeds of bounded rational leader increase to a critical value, and a larger quantum entanglement will enhance the stability of the quantum Stackelberg duopoly system. Numerical simulations demonstrate the complex dynamic features via bifurcation, largest Lyapunov exponent, fractal dimensions, strange attractors and sensitivity to initial conditions.

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Acknowledgements

The authors gratefully acknowledge two anonymous reviewers and Editor-in-Chief Yaakov S. Weinstein for their constructive comments and valuable suggestions. This research work is supported by Humanities and Social Science Projects of Ministry of Education of China (Grant No. 21YJA630116). The Foundation of the Educational Department of Liaoning Province (Grant No. LF201783613).

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Authors and Affiliations

  1. School of Mathematics, Liaoning Normal University, Dalian, 116029, China

    Xinli Zhang, Chao Yang, Yihan Wang & Shuning Zhang

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  1. Xinli Zhang
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  2. Chao Yang
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  3. Yihan Wang
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  4. Shuning Zhang
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Zhang, X., Yang, C., Wang, Y. et al. The influence of entanglement on complex dynamics of a quantum Stackelberg duopoly with heterogeneous expectations. Quantum Inf Process 21, 56 (2022). https://doi.org/10.1007/s11128-021-03395-4

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