IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v502y2018icp123-134.html
   My bibliography  Save this article

Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations

Author

Listed:
  • Quan, Ji
  • Liu, Wei
  • Chu, Yuqing
  • Wang, Xianjia

Abstract

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation.

Suggested Citation

  • Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    • Handle: RePEc:eee:phsmap:v:502:y:2018:i:c:p:123-134
    DOI: 10.1016/j.physa.2018.02.101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118301882
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.02.101?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. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
    2. Keke Huang & Tao Wang & Yuan Cheng & Xiaoping Zheng, 2015. "Effect of Heterogeneous Investments on the Evolution of Cooperation in Spatial Public Goods Game," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-10, March.
    3. Zhou, Tianwei & Ding, Shuai & Fan, Wenjuan & Wang, Hao, 2016. "An improved public goods game model with reputation effect on the spatial lattices," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 130-135.
    4. Valverde, Pablo A. & da Silva, Roberto & Stock, Eduardo V., 2017. "Global oscillations in the Optional Public Goods Game under spatial diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 61-69.
    5. Martin Sefton & Robert Shupp & James M. Walker, 2007. "The Effect Of Rewards And Sanctions In Provision Of Public Goods," Economic Inquiry, Western Economic Association International, vol. 45(4), pages 671-690, October.
    6. Astrid Dannenberg & Andreas Lange & Bodo Sturm, 2014. "Participation and Commitment in Voluntary Coalitions to Provide Public Goods," Economica, London School of Economics and Political Science, vol. 81(322), pages 257-275, April.
    7. Jennifer C. Coats & William S. Neilson, 2005. "Beliefs About Other-Regarding Preferences in a Sequential Public Goods Game," Economic Inquiry, Western Economic Association International, vol. 43(3), pages 614-622, July.
    8. Hang Ye & Fei Tan & Mei Ding & Yongmin Jia & Yefeng Chen, 2011. "Sympathy and Punishment: Evolution of Cooperation in Public Goods Game," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 14(4), pages 1-20.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    11. Yan Zhou & Peiran Jiao & Qilin Zhang, 2017. "Second-party and third-party punishment in a public goods experiment," Applied Economics Letters, Taylor & Francis Journals, vol. 24(1), pages 54-57, January.
    12. Dominic D. P. Johnson & Pavel Stopka & Stephen Knights, 2003. "The puzzle of human cooperation," Nature, Nature, vol. 421(6926), pages 911-912, February.
    13. 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.
    14. David G. Rand & Martin A. Nowak, 2011. "The evolution of antisocial punishment in optional public goods games," Nature Communications, Nature, vol. 2(1), pages 1-7, September.
    15. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    16. Ernst Fehr & Urs Fischbacher, "undated". "Third Party Punishment and Social Norms," IEW - Working Papers 106, Institute for Empirical Research in Economics - University of Zurich.
    17. Fangfang Tan, 2008. "Punishment in a Linear Public Good Game with Productivity Heterogeneity," De Economist, Springer, vol. 156(3), pages 269-293, September.
    18. Matthias Greiff, 2013. "Rewards and the private provision of public goods on dynamic networks," Journal of Evolutionary Economics, Springer, vol. 23(5), pages 1001-1021, November.
    19. Colasante, Annarita, 2017. "Selection of the distributional rule as an alternative tool to foster cooperation in a Public Good Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 482-492.
    20. Tian, Liang, 2012. "Temporal behavior of evolutionary dynamics in finite dimensional population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1234-1242.
    21. Cartwright, Edward & Stepanova, Anna, 2015. "The consequences of a refund in threshold public good games," Economics Letters, Elsevier, vol. 134(C), pages 29-33.
    22. Amir, Madjid & Berninghaus, Siegfried K., 1996. "Another Approach to Mutation and Learning in Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 19-43, May.
    23. Sekiguchi, Takuya, 2013. "General conditions for strategy abundance through a self-referential mechanism under weak selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2886-2892.
    24. Song, Qi-Qing & Li, Zhen-Peng & Fu, Chang-He & Wang, Lai-Sheng, 2011. "Optional contributions have positive effects for volunteering public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4236-4243.
    25. Shen, Chen & Lu, Jun & Shi, Lei, 2016. "Does coevolution setup promote cooperation in spatial prisoner's dilemma game?," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 201-207.
    26. Liu, Xuesong & He, Mingfeng & Kang, Yibin & Pan, Qiuhui, 2017. "Fixation of strategies with the Moran and Fermi processes in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 336-344.
    27. Gill, Wonpyong, 2009. "Fixation probability and the crossing time in the Wright–Fisher multiple alleles model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3124-3132.
    28. Wang, Jing & Chen, Xiaojie & Wang, Long, 2010. "Effects of migration on the evolutionary game dynamics in finite populations with community structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 67-78.
    29. Yang, Han-Xin & Rong, Zhihai, 2015. "Mutual punishment promotes cooperation in the spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 230-234.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Quan, Ji & Tang, Caixia & Wang, Xianjia, 2021. "Reputation-based discount effect in imitation on the evolution of cooperation in spatial public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    2. Lv, Ran & Qian, Jia-Li & Hao, Qing-Yi & Wu, Chao-Yun & Guo, Ning & Ling, Xiang, 2023. "The impact of current and historical reputation with non-uniform change on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2021. "Effect of reputation-based heterogeneous investment on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Gao, Liyan & Pan, Qiuhui & He, Mingfeng, 2020. "Changeable updating rule promotes cooperation in well-mixed and structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    5. 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).
    6. 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).
    7. Quan, Ji & Yang, Wenjun & Li, Xia & Wang, Xianjia & Yang, Jian-Bo, 2020. "Social exclusion with dynamic cost on the evolution of cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    8. Quan, Ji & Tang, Caixia & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

    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. 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.
    2. Quan, Ji & Tang, Caixia & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Quan, Ji & Tang, Caixia & Wang, Xianjia, 2021. "Reputation-based discount effect in imitation on the evolution of cooperation in spatial public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    4. Xie, Kai & Liu, Xingwen & Chen, Hao & Yang, Jun, 2022. "Preferential selection and expected payoff drive cooperation in spatial voluntary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    5. Wang, Yongjie & Chen, Tong & Chen, Qiao & Si, Guangrun, 2017. "Emotional decisions in structured populations for the evolution of public cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 475-481.
    6. Wang, Yongjie & Chen, Tong, 2015. "Heuristics guide cooperative behaviors in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 59-65.
    7. Shang, Lihui & Sun, Sihao & Ai, Jun & Su, Zhan, 2022. "Cooperation enhanced by the interaction diversity for the spatial public goods game on regular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    8. Gangadharan, Lata & Nikiforakis, Nikos & Villeval, Marie Claire, 2017. "Normative conflict and the limits of self-governance in heterogeneous populations," European Economic Review, Elsevier, vol. 100(C), pages 143-156.
    9. Jin, Jiahua & Shen, Chen & Chu, Chen & Shi, Lei, 2017. "Incorporating dominant environment into individual fitness promotes cooperation in the spatial prisoners' dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 70-75.
    10. Song, Qun & Cao, Zhaoheng & Tao, Rui & Jiang, Wei & Liu, Chen & Liu, Jinzhuo, 2020. "Conditional neutral punishment promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    11. Wang, Mie & Kang, HongWei & Shen, Yong & Sun, XingPing & Chen, QingYi, 2021. "The role of alliance cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. 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).
    13. Hong, Lijun & Geng, Yini & Du, Chunpeng & Shen, Chen & Shi, Lei, 2021. "Average payoff-driven or imitation? A new evidence from evolutionary game theory in finite populations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    14. Chen, Qiao & Chen, Tong & Wang, Yongjie, 2017. "Publishing the donation list incompletely promotes the emergence of cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 48-56.
    15. Zhu, Wenqiang & Pan, Qiuhui & Song, Sha & He, Mingfeng, 2023. "Effects of exposure-based reward and punishment on the evolution of cooperation in prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    16. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    17. Peng Lu & Xiaoping Zheng, 2015. "Social Stratification and Cooperative Behavior in Spatial Prisoners' Dilemma Games," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    18. Wang, Jianwei & Yu, Fengyuan & He, Jialu & Chen, Wei & Xu, Wenshu & Dai, Wenhui & Ming, Yuexin, 2023. "Promotion, Disintegration and Remediation of group cooperation under heterogeneous distribution system based on peer rating," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    19. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Li, Tong & Yu, Yong, 2018. "Synergy punishment promotes cooperation in spatial public good game," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 214-218.
    20. Quan, Ji & Yu, Junyu & Li, Xia & Wang, Xianjia, 2023. "Conditional switching between social excluders and loners promotes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

    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:phsmap:v:502:y:2018:i:c:p:123-134. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.