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The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma

Author

Listed:
  • Zhiyuan Dong

    (School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen 150001, China
    These authors contributed equally to this work.)

  • Ai-Guo Wu

    (School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen 150001, China
    These authors contributed equally to this work.)

Abstract

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N -player case. The final state of quantum game theory of N -player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.

Suggested Citation

  • Zhiyuan Dong & Ai-Guo Wu, 2021. "The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma," Mathematics, MDPI, vol. 9(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1443-:d:578718
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    References listed on IDEAS

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    1. Erica Klarreich, 2001. "Playing by quantum rules," Nature, Nature, vol. 414(6861), pages 244-245, November.
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