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

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  • 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
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    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.
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    Cited by:

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    6. 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).
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