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The effect of nonlinear environmental feedback on the outcomes of evolutionary dynamics

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  • Huang, Jiaquan
  • Zhu, Yuying
  • Xia, Chengyi
  • Tanimoto, Jun

Abstract

In this paper, we construct a nonlinear evolutionary game model to analyze the cooperation mechanisms of the population based on a nonlinear relationship among environment and strategies. In the model, replicator dynamics and aspiration dynamics are used to explore the evolutionary outcomes of collective decision, respectively. The results suggest that the environment tends to become progressively more affluent as the number of cooperators increases, if there is a smaller intensity of environmental destruction of defectors. Interestingly, the enriched environments may attract more defectors. Hence, the population requires a higher level of vigilance against plentiful environments in response to the emergence of defectors. As opposed to replicator dynamics, aspiration dynamics can avoid the persistent oscillatory loops due to the level of aspiration. Further, we investigate the effect of complexity between the population strategy and the environment on the evolutionary outcomes. It is found that higher level of complexity can drive the environment closer to a state of affluence, but the population's strategy structure will not be modified. These insights into the relationship between environment and strategies further our understanding of the evolutionary mechanism of population and society.

Suggested Citation

  • Huang, Jiaquan & Zhu, Yuying & Xia, Chengyi & Tanimoto, Jun, 2024. "The effect of nonlinear environmental feedback on the outcomes of evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 483(C).
    • Handle: RePEc:eee:apmaco:v:483:y:2024:i:c:s009630032400451x
    DOI: 10.1016/j.amc.2024.128990
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    1. Brander, James A & Taylor, M Scott, 1998. "The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use," American Economic Review, American Economic Association, vol. 88(1), pages 119-138, March.
    2. Liu, Fanglin & Wu, Bin, 2022. "Environmental quality and population welfare in Markovian eco-evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    3. Cheng, Haihui & Meng, Xinzhu, 2023. "Multistability and Hopf bifurcation analysis for a three-strategy evolutionary game with environmental feedback and delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 620(C).
    4. Zhen Wang & Marko Jusup & Lei Shi & Joung-Hun Lee & Yoh Iwasa & Stefano Boccaletti, 2018. "Exploiting a cognitive bias promotes cooperation in social dilemma experiments," Nature Communications, Nature, vol. 9(1), pages 1-7, December.
    5. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Yan, Fang & Hou, Xiaorong & Tian, Tingting & Chen, Xiaojie, 2023. "Nonlinear model reference adaptive control approach for governance of the commons in a feedback-evolving game," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. repec:nas:journl:v:115:y:2018:p:30-35 is not listed on IDEAS
    8. Cheng, Haihui & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2023. "Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Guo, Yujie & Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2023. "Network adaption based on environment feedback promotes cooperation in co-evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    10. Andrew R. Tilman & Joshua B. Plotkin & Erol Akçay, 2020. "Evolutionary games with environmental feedbacks," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    11. Yu, Yanan & He, Yong & Zhao, Xuan, 2021. "Impact of demand information sharing on organic farming adoption: An evolutionary game approach," Technological Forecasting and Social Change, Elsevier, vol. 172(C).
    12. Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2022. "Migration based on environment comparison promotes cooperation in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    13. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2023. "Evolution of cooperation with nonlinear environment feedback in repeated public goods game," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    14. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    15. Christian Hilbe & Štěpán Šimsa & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Evolution of cooperation in stochastic games," Nature, Nature, vol. 559(7713), pages 246-249, July.
    Full references (including those not matched with items on IDEAS)

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