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Winner-weaken-loser-strengthen rule leads to optimally cooperative interdependent networks

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Abstract

We introduce a winner-weaken-loser-strengthen rule and study its effects on how cooperation evolves on interdependent networks. The new rule lowers the learning ability of a player if its payoff is larger than the average payoff of its neighbors, thus enhancing its chance to hold onto its current strategy. Conversely, when a player gaining less than the average payoff of its neighborhood, its learning ability is increased, thus weakening the player by increasing the chance of strategy change. Furthermore, considering the nature of human pursue fairness, we let a loser, someone who has larger learning ability, can benefit from another network, whereas a winner cannot. Our results show that moderate values of the threshold lead to a high cooperation plateau, while too high or too small values of the threshold inhibit cooperation. At moderate thresholds, the flourishing cooperation is attributed to species diversity and equality, whereas a lacking of species diversity determines the vanishing of cooperation. We thus demonstrate that a simple winner-weaken-loser-strengthen rule significantly expands the scope of cooperation on structured populations.

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Acknowledgements

We are grateful to Dr. Keke Huang for useful discussions. We acknowledge support from (i) National Natural Science Foundation of China (Grants No. U1803263), the National 1000 Young Talent Plan (No. W099102), the Fundamental Research Funds for the Central Universities (No. 3102017jc03007) and China Computer Federation - Tencent Open Fund (No. IAGR20170119) to Z.W, (ii) the National Natural Science Foundation of China (Grants No. 11671348) to L.S., (iii) the Yunnan Postgraduate Scholarship Award to C.S. and (iv) the Slovenian Research Agency (Grants J1-7009, J1-9112 and P1-0403) to M.P.

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    Authors and Affiliations

    1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, Yunnan, China

      Lei Shi, Chen Shen, Yini Geng & Chen Chu

    2. School of Software, Yunnan University, Kunming, 650504, Yunnan, China

      Haoran Meng

    3. Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000, Maribor, Slovenia

      Matjaž Perc

    4. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, 2000, Maribor, Slovenia

      Matjaž Perc

    5. Complexity Science Hub Vienna, Josefstädterstraße 39, 1080, Vienna, Austria

      Matjaž Perc

    6. CNR Institute for Complex Systems, Via Madonna del Piano 10, 50019, Florence, Italy

      Stefano Boccaletti

    7. Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi’an, 710072, China

      Stefano Boccaletti

    8. School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an, 710072, China

      Zhen Wang

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    1. Lei Shi
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    L. Shi and C. Shen contributed equally to this work.

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    Shi, L., Shen, C., Geng, Y. et al. Winner-weaken-loser-strengthen rule leads to optimally cooperative interdependent networks. Nonlinear Dyn 96, 49–56 (2019). https://doi.org/10.1007/s11071-019-04772-6

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    • DOI: https://doi.org/10.1007/s11071-019-04772-6

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