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A Proportional-Egalitarian Allocation Policy for Public Goods Problems with Complex Network

Author

Listed:
  • Guang Zhang

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Nan He

    (Business School, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Yanxia Dong

    (School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China)

Abstract

How free-riding behavior can be avoided is a constant topic in public goods problems, especially in persistent and complex resource allocation situations. In this paper, a novel allocation policy for public goods games with a complex network, called the proportional-egalitarian allocation method (PEA), is proposed. This allocation rule differs from the well-studied redistribution policies by following a two-step process without paying back into the common pool. A parameter is set up for dividing the total income into two parts, and then they are distributed by following the egalitarianism and proportional rule, respectively. The first part of total income is distributed equally, while the second part is allocated proportionally according to players’ initial payoffs. In addition, a new strategy-updating mechanism is proposed by comparing the average group payoffs instead of the total payoffs. Compared with regular lattice networks, this mechanism admits the difference of cooperative abilities among players induced by the asymmetric network. Furthermore, numerical calculations show that a relatively small income for the first distribution step will promote the cooperative level, while relatively less income for the second step may harm cooperation evolution. This work thus enriches the knowledge of allocation policies for public goods games and also provides a fresh perspective for the strategy-updating mechanism.

Suggested Citation

  • Guang Zhang & Nan He & Yanxia Dong, 2021. "A Proportional-Egalitarian Allocation Policy for Public Goods Problems with Complex Network," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2034-:d:620906
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    References listed on IDEAS

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    1. Zhang, Jianlei & Zhang, Chunyan & Chu, Tianguang, 2011. "The evolution of cooperation in spatial groups," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 131-136.
    2. Xia, Cheng-yi & Ma, Zhi-qin & Wang, Zhen & Wang, Juan, 2012. "Evaluating fitness by integrating the highest payoff within the neighborhood promotes cooperation in social dilemmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6440-6447.
    3. Yang, Han-Xin & Yang, Jing, 2019. "Reputation-based investment strategy promotes cooperation in public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 886-893.
    4. 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).
    5. Botelho, Anabela & Harrison, Glenn W. & Pinto, Lígia M. Costa & Rutström, Elisabet E., 2009. "Testing static game theory with dynamic experiments: A case study of public goods," Games and Economic Behavior, Elsevier, vol. 67(1), pages 253-265.3, September.
    6. Fronczak, Agata & Hołyst, Janusz A & Jedynak, Maciej & Sienkiewicz, Julian, 2002. "Higher order clustering coefficients in Barabási–Albert networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 688-694.
    7. Gao, Bo & liu, Xuan & Hou, Shuxia & Jia, Danyang & Du, Mingjing, 2019. "Resolving public goods dilemma by giving the poor more support," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    8. Chunpeng Du & Danyang Jia & Libin Jin & Lei Shi, 2018. "The impact of neutral reward on cooperation in public good game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(10), pages 1-6, October.
    9. 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).
    10. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    11. Wang, Qiang & He, Nanrong & Chen, Xiaojie, 2018. "Replicator dynamics for public goods game with resource allocation in large populations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 162-170.
    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. Gao, Bo & Deng, Zheng-hong & Zhao, Da-wei & Song, Qun, 2017. "State analysis of Boolean control networks with impulsive and uncertain disturbances," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 187-192.
    14. 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.
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    1. Xiaopeng Li & Zhonglin Wang & Jiuqiang Liu & Guihai Yu, 2023. "The Sense of Cooperation on Interdependent Networks Inspired by Influence-Based Self-Organization," Mathematics, MDPI, vol. 11(4), pages 1-16, February.

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