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Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy

Author

Listed:
  • Zhou, Die
  • Pi, Jinxiu
  • Yang, Guanghui
  • Yang, Hui

Abstract

This paper first builds a nonlinear dynamic system of the Commons’ tragedy with quantum strategies in discrete time. There are two heterogeneous expectations in the game, namely, one of the two players is boundedly rational and the other is of adaptive expectation. Secondly, we obtain a sufficient and necessary condition for quantum Nash equilibria to be stable equilibria. Finally, we investigate the impacts of quantum entanglement on the stable region of systems and analyze the behaviors of complex dynamical systems. The results show that quantum Nash equilibria are stable points of nonlinear dynamics for quantum Commons’ tragedy if both quantum entanglement and quantum strategy adjustment speed satisfy certain conditions. In addition, numerical simulations discuss the features of nonlinear dynamics, such as bifurcation, the largest Lyapunov exponent, fractal dimension, strange attractor, and sensitivity to initial conditions. The numerical results show that nonlinear dynamics appear chaotic if the adjustment speed of quantum strategy or the quantum entanglement degree is larger.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:608:y:2022:i:p1:s0378437122007890
    DOI: 10.1016/j.physa.2022.128231
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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. Lian Shi & Yun Le & Zhaohan Sheng, 2014. "Analysis of Price Stackelberg Duopoly Game with Bounded Rationality," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, February.
    3. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2009. "The dynamics of Bertrand model with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2048-2055.
    4. Peng, Yu & Lu, Qian, 2015. "Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 259-268.
    5. 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.
    6. Alonso-Sanz, Ramón, 2019. "Simulation of the quantum Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    7. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    8. Salman Khan & M. Ramzan & M. K. Khan, 2010. "Quantum Model of Bertrand Duopoly," Papers 1001.2831, arXiv.org, revised Oct 2010.
    9. 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).
    10. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    Full references (including those not matched with items on IDEAS)

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