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Two population three-player prisoner’s dilemma game

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  • EL-Seidy, Essam
  • Elshobaky, Entisarat.M.
  • Soliman, Karim.M.

Abstract

Due to the computational advantage in symmetric games, most researches have focused on the symmetric games instead of the asymmetric ones which need more computations. In this paper, we present prisoner’s dilemma game involving three players, and suppose that two players among them agree against the third player by choosing either to cooperate together or to defect together at each round. According to that assumption, the game is transformed from the symmetric three- player model to asymmetric two-player model such that, the identities of the players cannot be interchanged without interchanging the payoff of the strategies. Each strategy in the resulting model is expressed with two state automata. We determine the payoff matrix corresponding to the all possible strategies. We noticed that, for some strategies, it is better to be a player of the first type (independent player) than being of the second type (allies).

Suggested Citation

  • EL-Seidy, Essam & Elshobaky, Entisarat.M. & Soliman, Karim.M., 2016. "Two population three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 44-53.
    • Handle: RePEc:eee:apmaco:v:277:y:2016:i:c:p:44-53
    DOI: 10.1016/j.amc.2015.12.047
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    3. El-Seidy, Essam & Soliman, Karim.M., 2016. "Iterated symmetric three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 117-127.
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    Cited by:

    1. Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Zhang, Yifan & Shu, Gang & Li, Ya, 2017. "Strategy-updating depending on local environment enhances cooperation in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 224-232.
    3. Li, Dandan & Zhou, Kai & Sun, Mei & Han, Dun, 2023. "Investigating the effectiveness of individuals’ historical memory for the evolution of the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. El-Salam, Salsabeel M. Abd & El-Seidy, Essam & Abdel-Malek, Amira R., 2023. "Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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