IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v142y2021ics0960077920308821.html
   My bibliography  Save this article

Average abundance function of multi-player threshold public goods without initial endowment evolutionary game model under differential aspiration levels and redistribution mechanism

Author

Listed:
  • 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.We explore the characteristics of average abundance function XA(ω) based on threshold public goods evolutionary game model without initial endowment under differential aspiration levels and redistribution mechanism by analytical analysis and numerical simulation. The main work contains four aspects. (1) We deduce the concrete expression of expected payoff function. We also obtain the intuitive expression of average abundance function on the basis of detailed balance condition. (2) We have deduced the approximate expressions of average abundance function when selection intensity is sufficient small. (3) We have deduced the approximate expressions of average abundance function when selection intensity is large enough. The range of summation for average abundance function will be reduced because of this approximation expression. (4) We analyze the influence of the size of group d, multiplication factor r, and cost c on average abundance function through numerical simulation. On one hand, when selection intensity is small, the influence of parameters on average abundance function is slight. On the other hand, when selection intensity is large, average abundance function will decrease with d. The average abundance function will decrease at first, and then increase quickly with the increase of r if threshold m=4. The average abundance function will decrease slowly at first, and then increase with the increase of r if threshold m=9. The average abundance function will decrease with the increase of c if threshold m=4. The average abundance function will remain unchanged at first, then increase, at last it will remain stable with the increase of c if threshold m=9. Furthermore, these conclusions have been explained based on expected payoff function π(·) and function h(i,ω).

Suggested Citation

  • Xia, Ke, 2021. "Average abundance function of multi-player threshold public goods without initial endowment evolutionary game model under differential aspiration levels and redistribution mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308821
    DOI: 10.1016/j.chaos.2020.110490
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920308821
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110490?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. 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.
    5. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    6. 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.
    7. 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.
    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-Qin Ma & Cheng-Yi Xia & Shi-Wen Sun & Li Wang & Huai-Bin Wang & Juan Wang, 2011. "Heterogeneous Link Weight Promotes The Cooperation In Spatial Prisoner'S Dilemma," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(11), pages 1257-1268.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Tian, Lin-Lin & Li, Ming-Chu & Lu, Kun & Zhao, Xiao-Wei & Wang, Zhen, 2013. "The influence of age-driven investment on cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 65-70.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Wang, Si-Yi & Liu, Yan-Ping & Zhang, Feng & Wang, Rui-Wu, 2021. "Super-rational aspiration induced strategy updating promotes cooperation in the asymmetric prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Wang, Yi-Ling, 2013. "Asymmetric evaluation of fitness enhances spatial reciprocity in social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 76-81.
    4. Wang, Yi-Ling, 2013. "Learning ability driven by majority selection enhances spatial reciprocity in prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 96-100.
    5. Du, Jinming & Wu, Ziren, 2023. "Coevolutionary dynamics of strategy and network structure with publicity mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    6. Xia, Chengyi & Miao, Qin & Zhang, Juanjuan, 2013. "Impact of neighborhood separation on the spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 22-30.
    7. Quan, Ji & Yang, Xiukang & Wang, Xianjia, 2018. "Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 973-983.
    8. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Information fusion based on reputation and payoff promotes cooperation in spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    9. Lu, Peng, 2015. "Individual choice and reputation distribution of cooperative behaviors among heterogeneous groups," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 39-46.
    10. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Evidential reasoning based on imitation and aspiration information in strategy learning promotes cooperation in optional spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    11. Li, Cong & Xu, Hedong & Fan, Suohai, 2020. "Synergistic effects of self-optimization and imitation rules on the evolution of cooperation in the investor sharing game," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    12. Wang, Lei & Xia, Chengyi & Wang, Li & Zhang, Ying, 2013. "An evolving Stag-Hunt game with elimination and reproduction on regular lattices," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 69-76.
    13. Xia, Chengyi & Wang, Juan & Wang, Li & Sun, Shiwen & Sun, Junqing & Wang, Jinsong, 2012. "Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1239-1245.
    14. Wu, Yu’e & Zhang, Zhipeng & Yang, Guoli & Liu, Haixin & Zhang, Qingfeng, 2022. "Evolution of cooperation driven by diversity on a double-layer square lattice," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    15. Sun, Peiyuan & Liu, Xuesong & Wang, Enze & He, Mingfeng & Pan, Qiuhui, 2017. "Evolution of cooperation in a spatial structure with compensation mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 503-507.
    16. Wang, Lei & Wang, Juan & Guo, Baohong & Ding, Shuai & Li, Yukun & Xia, Chengyi, 2014. "Effects of benefit-inspired network coevolution on spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 9-16.
    17. Hu, Menglong & Wang, Juan & Kong, Lingcong & An, Kang & Bi, Tao & Guo, Baohong & Dong, Enzeng, 2015. "Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 47-52.
    18. Bin Wu & Julián García & Christoph Hauert & Arne Traulsen, 2013. "Extrapolating Weak Selection in Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 9(12), pages 1-7, December.
    19. Yang, Luhe & Zhang, Lianzhong & Yang, Duoxing, 2022. "Asymmetric micro-dynamics in spatial anonymous public goods game," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    20. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308821. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.