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Quantum Model of Bertrand Duopoly

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  • Salman Khan
  • M. Ramzan
  • M. K. Khan

Abstract

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entanglement in the initial state gives payoffs higher to the firms than the classical payoffs at the Nash equilibrium. As a result the dilemma like situation in the classical game is resolved.

Suggested Citation

  • Salman Khan & M. Ramzan & M. K. Khan, 2010. "Quantum Model of Bertrand Duopoly," Papers 1001.2831, arXiv.org, revised Oct 2010.
    • Handle: RePEc:arx:papers:1001.2831
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    Cited by:

    1. Alonso-Sanz, Ramon & Adamatzky, Andrew, 2020. "Spatial simulation of the quantum Bertrand duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Zhang, Cuihua & Xing, Peng, 2015. "A research on service quality decision-making of Chinese communications industry based on quantum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 9-15.
    3. 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).
    4. 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).

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