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Quantum Prisoner’s Dilemma in Asymmetric Strategy Spaces

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Abstract

Most games in the real world are asymmetric, and participants can have different conditions or strategies, depending on the available resources. In this work, the quantum prisoner’s dilemma with two dilemma strength parameters is studied. Two examples of asymmetric strategy spaces are considered. We show that, most of the obtained Nash equilibria are not Pareto optimal. Therefore, the classical dilemma can still exist in the quantum regime with asymmetric strategy spaces. These results can be applied to real-world situations, when global issues requiring the interaction of agents from different environments exist.

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Acknowledgements

The authors are very grateful to the reviewer for the helpful suggestions.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Arish University, Arish, 45516, Egypt

    A. S. Elgazzar

  2. Mathematics Department, Faculty of Science, Damietta University, New Damietta, Egypt

    H. A. Elrayes

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  1. A. S. Elgazzar
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  2. H. A. Elrayes
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Correspondence to A. S. Elgazzar.

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Elgazzar, A.S., Elrayes, H.A. Quantum Prisoner’s Dilemma in Asymmetric Strategy Spaces. Int J Theor Phys 60, 3467–3477 (2021). https://doi.org/10.1007/s10773-021-04913-x

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