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The characteristics of average abundance function of multi-player threshold public goods evolutionary game model under redistribution mechanism

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  • Xia, Ke

Abstract

The average abundance function reflects the level of cooperation in the population. So it is important to analyze how to increase the average abundance function in order to facilitate the proliferation of cooperative behavior. The characteristics of average abundance function based on multi-player threshold public goods evolutionary game model under redistribution mechanism have been explored by analytical analysis and numerical simulation in this article. The main research findings contain four aspects. Firstly, we deduce the concrete expression of expected payoff function. In addition, we obtain the intuitive expression of average abundance function by taking the detailed balance condition as the point of penetration. Secondly, we obtain the approximate expression of average abundance function when selection intensity is sufficient small. In this case, average abundance function can be simplified from composite function to linear function. In addition, this conclusion will play a significant role when analyzing the results of the numerical simulation. Thridly, we deduce the approximate expression of average abundance function when selection intensity is large enough. Because of this approximation expression, the range of summation will be reduced, the number of operations for average abundance function will be reduced, and the operating efficiency for numerical simulation will be improved. Fourthly, we explore the influences of parameters (the size of group d, multiplication factor r, cost c, aspiration level α and the proportion of income redistribution τ) on the average abundance function through numerical simulation. Also the corresponding results have been explained based on the expected payoff function and function h(i, ω). It can be concluded that when selection intensity ω is small, the effects of parameters (d, r, c, α and τ) on average abundance function is slight. When selection intensity ω is large, there will be five conditions. (1) Average abundance function will decrease with d regardless of whether threshold m is small or large. (2) Average abundance function will decrease at first and then increase with r when threshold m is small. Average abundance function will increase with r when threshold m is large. (3) Average abundance function will basically remain unchanged with c regardless of whether threshold m is small or large. (4) Average abundance function will remain stable at first and then increase with α when threshold m is small. Average abundance function will remain stable at first and then decrease with α when threshold m is large. It should be noted that average abundance function will get close to 1/2 when α is large enough. (5) Average abundance function will increase with τ regardless of whether threshold m is small or large.

Suggested Citation

  • Xia, Ke, 2021. "The characteristics of average abundance function of multi-player threshold public goods evolutionary game model under redistribution mechanism," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s009630032030686x
    DOI: 10.1016/j.amc.2020.125733
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    1. Lin, Hai & Yang, Dong-Ping & Shuai, J.W., 2011. "Cooperation among mobile individuals with payoff expectations in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 153-159.
    2. Bin Wu & Arne Traulsen & Chaitanya S. Gokhale, 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations," Games, MDPI, vol. 4(2), pages 1-18, May.
    3. Zhi Li & Zhihu Yang & Te Wu & Long Wang, 2014. "Aspiration-Based Partner Switching Boosts Cooperation in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-7, June.
    4. Li, Ming & Jia, Chun-Xiao & Liu, Run-Ran & Wang, Bing-Hong, 2013. "Emergence of cooperation in spatial public goods game with conditional participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1840-1847.
    5. Bin Wu & Lei Zhou, 2018. "Individualised aspiration dynamics: Calculation by proofs," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-15, September.
    6. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    7. Chen, Xiaojie & Fu, Feng & Wang, Long, 2008. "Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5609-5615.
    8. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    9. Zhi-Hai Rong & Qian Zhao & Zhi-Xi Wu & Tao Zhou & Chi Kong Tse, 2016. "Proper aspiration level promotes generous behavior in the spatial prisoner’s dilemma game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(7), pages 1-7, July.
    10. Wang, Xiaofeng & Chen, Xiaojie & Gao, Jia & Wang, Long, 2013. "Reputation-based mutual selection rule promotes cooperation in spatial threshold public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 181-187.
    11. Yu Peng & Xu-Wen Wang & Qian Lu & Qing-Ke Zeng & Bing-Hong Wang, 2014. "Effects of aspiration-induced adaptation and migration on the evolution of cooperation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(07), pages 1-12.
    12. Weijun Zeng & Minqiang Li & Nan Feng, 2017. "The effects of heterogeneous interaction and risk attitude adaptation on the evolution of cooperation," Journal of Evolutionary Economics, Springer, vol. 27(3), pages 435-459, July.
    13. Du, Jinming, 2019. "Redistribution promotes cooperation in spatial public goods games under aspiration dynamics," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    14. Zhang, Jun & Fang, Yi-Ping & Du, Wen-Bo & Cao, Xian-Bin, 2011. "Promotion of cooperation in aspiration-based spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2258-2266.
    15. Yakushkina, Tatiana & Saakian, David B., 2018. "New versions of evolutionary models with lethal mutations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 470-477.
    16. Yongkui Liu & Xiaojie Chen & Lin Zhang & Long Wang & Matjaž Perc, 2012. "Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-8, February.
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