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Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks

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  • Angsheng Li
  • Xi Yong

Abstract

Recently, the authors proposed a quantum prisoner’s dilemma game based on the spatial game of Nowak and May, and showed that the game can be played classically. By using this idea, we proposed three generalized prisoner’s dilemma (GPD, for short) games based on the weak Prisoner’s dilemma game, the full prisoner’s dilemma game and the normalized Prisoner’s dilemma game, written by GPDW, GPDF and GPDN respectively. Our games consist of two players, each of which has three strategies: cooperator (C), defector (D) and super cooperator (denoted by Q), and have a parameter γ to measure the entangled relationship between the two players. We found that our generalised prisoner’s dilemma games have new Nash equilibrium principles, that entanglement is the principle of emergence and convergence (i.e., guaranteed emergence) of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that entanglement provides a threshold for a phase transition of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that the role of heterogeneity of the scale-free networks in cooperations and super cooperations is very limited, and that well-defined structures of scale-free networks allow coexistence of cooperators and super cooperators in the evolutions of the weak version of our generalised prisoner’s dilemma games.

Suggested Citation

  • Angsheng Li & Xi Yong, 2015. "Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-24, February.
    • Handle: RePEc:plo:pone00:0116429
    DOI: 10.1371/journal.pone.0116429
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    References listed on IDEAS

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    1. James M Chappell & Azhar Iqbal & Derek Abbott, 2011. "Analyzing Three-Player Quantum Games in an EPR Type Setup," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-11, July.
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    4. Li, Qiang & Iqbal, Azhar & Chen, Minyou & Abbott, Derek, 2012. "Quantum strategies win in a defector-dominated population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3316-3322.
    5. Pawela, Łukasz & Sładkowski, Jan, 2013. "Quantum Prisoner’s Dilemma game on hypergraph networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 910-917.
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    2. Deng, Yunsheng & Zhang, Jihui, 2021. "The role of the preferred neighbor with the expected payoff on cooperation in spatial public goods game under optimal strategy selection mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).

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