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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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    File URL: http://arxiv.org/pdf/1001.2831
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    References listed on IDEAS

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    1. Austin Gerig, 2008. "A Theory for Market Impact: How Order Flow Affects Stock Price," Papers 0804.3818, arXiv.org, revised Jul 2008.
    2. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    3. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
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    Cited by:

    1. 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.

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