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Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game

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  • Taha, Mohammad A.
  • Ghoneim, Ayman

Abstract

The “iterated prisoner's dilemma” (IPD) game is considered to be a well-known model for studying the evolution of cooperative manner among rational individuals over the long term. Analytical studies in IPD mostly focus on the two-player IPD game since the game's relations and dynamics become more complicated when increasing players' numbers. Here, we extend investigating the “Zero-Determinant” (ZD) strategies to the symmetric infinitely repeated IPD game involving three players with two actions for each player. We propose two simultaneous models of the IPD game with three players to investigate ZD strategies. Further, we analytically extract the boundaries of the equalizer and extortion ZD strategies in both proposed models and provide numerical examples demonstrating such boundaries.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007621
    DOI: 10.1016/j.chaos.2021.111408
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    References listed on IDEAS

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    Cited by:

    1. 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).
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    3. Li, Dandan & Sun, Xiaoxiao & He, Youxin & Han, Dun, 2022. "On prisoner’s dilemma game with psychological bias and memory learning," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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