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Environmental quality and population welfare in Markovian eco-evolutionary dynamics

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  • Liu, Fanglin
  • Wu, Bin

Abstract

Environmental change and human behavior are co-depended. The quality of the environment affects human’s welfare, and the human’s behavior in turn changes the environment. Yet the co-dependent nature seems to give a single individual few capabilities to change the environment. Intuitively, it is the collective actions that matter. What is a single individual able to do with the population welfare and the environment? We set up a toy model to explicitly address this issue. We take into account the eco-evolutionary nature of the feedback between environment and human behavior. One strategy, termed as Welfare-Time strategy, is found, using which one individual suffices to set a linear relationship between collective welfare and environmental quality, no matter what the opponent does. This linear relationship can be either positively or negatively correlated, which is also unilaterally set by a single individual. It indicates that collective welfare can be higher even if it takes longer in a poor environment. Furthermore, we prove that the Welfare-Time strategy is able to dominate Win-Stay-Lose-Shift strategy, which is evolutionary stable against many strategies in repeated games. Our work reveals a hidden relationship between population welfare and the environment quality, which can be controlled unilaterally by a single individual. In addition, it implies that a single individual is able to control the environmental quality, provided that the rule of the environmental dynamics is known.

Suggested Citation

  • Liu, Fanglin & Wu, Bin, 2022. "Environmental quality and population welfare in Markovian eco-evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003836
    DOI: 10.1016/j.amc.2022.127309
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    References listed on IDEAS

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    1. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    2. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. 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.
    4. 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.
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    Cited by:

    1. Liu, Yuan & Cao, Lixuan & Wu, Bin, 2022. "General non-linear imitation leads to limit cycles in eco-evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. 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).

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