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Quantum prisoner’s dilemma in a restricted one-parameter strategic space

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  • Elgazzar, Ahmed S.

Abstract

Choosing a suitable restricted strategic space is crucial for the novel features of quantum games. Based on the Eisert–Wilkens–Lewenstein quantization scheme, a quantum prisoner’s dilemma is introduced using a simple restricted one-parameter strategic space. Our scheme is found to preserve the quantum advantages of the Eisert–Wilkens–Lewenstein scheme, and improve its Nash equilibrium characteristics. The simplicity of the calculations enables us to address some important aspects of quantum games which can be applied to many real systems. The robustness of Nash equilibria to corruption in the initial state is studied, and a measure of robustness is defined. The robustness of Nash equilibria is found to scale inversely with the entanglement. Our scheme is applied to various prisoner’s dilemma games having different dilemma strength. Also, Some variant forms of restricted one-parameter strategic space are studied.

Suggested Citation

  • Elgazzar, Ahmed S., 2020. "Quantum prisoner’s dilemma in a restricted one-parameter strategic space," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319309191
    DOI: 10.1016/j.amc.2019.124927
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. E. Ahmed & A. S. Hegazi & A. S. Elgazzar, 2003. "Sato–Crutchfield Formulation For Some Evolutionary Games," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(07), pages 963-971.
    3. E. Ahmed & A. S. Elgazzar, 2000. "On Local Prisoner'S Dilemma Game With Pareto Updating Rule," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 1539-1544.
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