IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v509y2018icp817-826.html
   My bibliography  Save this article

Effects of inertia on the evolution of cooperation in the voluntary prisoner’s dilemma game

Author

Listed:
  • Jia, Danyang
  • Jin, Jiahua
  • Du, Chunpeng
  • Shi, Lei

Abstract

In this paper, we explore the effects of inertia on the evolution of cooperation in voluntary prisoner’s dilemma on a square lattice. In real life, individual inertia is hard to change due to the inherent characteristics of players. Only when he meets lazy and rich people, he will try to change his inertia. Inspired by this, the evolution of inertia is constructed as follows: initially each individual sets a different inertia value due to the heterogeneities among them. Considering loner is a risk averse player, we assume that he has the largest inertia during the simulation. Subsequently, as long as an individual encounters a loner and decides to change his strategy, he will learn his neighbor’s inertia simultaneously. Otherwise, his inertia will remain unchanged. Through a large number of simulations we find that, counterintuitively, individual inertia will impede cooperation. Especially, the larger value of inertia, the less likely the individual to change his strategy, and it severely weakened the effect of rock-scissor-paper cyclic dominance in promoting cooperation by making it happen less and less frequently, further leading to a full loner phase. For a comprehensive understanding, we give an explanation from macroscopic and microscopic aspects. Besides, we use a small-world network to verify the robustness of this mechanism. The results also suggest that individuals can maintain the diversity of the population only if they maintain appropriate enthusiasm to participate in social activities. Our work may provide further insight in understanding the role of inertia on the evolution of cooperation.

Suggested Citation

  • Jia, Danyang & Jin, Jiahua & Du, Chunpeng & Shi, Lei, 2018. "Effects of inertia on the evolution of cooperation in the voluntary prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 817-826.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:817-826
    DOI: 10.1016/j.physa.2018.06.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118307775
    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.2018.06.053?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. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    2. Ernst Fehr & Urs Fischbacher, "undated". "Why Social Preferences Matter - The Impact of Non-Selfish Motives on Competition," IEW - Working Papers 084, Institute for Empirical Research in Economics - University of Zurich.
    3. 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.
    4. Chang, Shuhua & Zhang, Zhipeng & Wu, Yu’e & Xie, Yunya, 2018. "Cooperation is enhanced by inhomogeneous inertia in spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 419-425.
    5. repec:hhs:iuiwop:487 is not listed on IDEAS
    6. F. Fu & L.-H. Liu & L. Wang, 2007. "Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(4), pages 367-372, April.
    7. Ernst Fehr & Urs Fischbacher, 2002. "Why Social Preferences Matter -- The Impact of Non-Selfish Motives on Competition, Cooperation and Incentives," Economic Journal, Royal Economic Society, vol. 112(478), pages 1-33, March.
    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. Wang, Dongqi & Shuai, Xuanyue & Pan, Qiuhui & Li, Jingye & Lan, Xiaolong & He, Mingfeng, 2020. "Long deliberation times promote cooperation in the prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Yu, Fengyuan & Wang, Jianwei & He, Jialu, 2022. "Inequal dependence on members stabilizes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Sun, Chengbin & Luo, Chao, 2020. "Co-evolution of limited resources in the memory-based spatial evolutionary game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Sun, Peng & Zhang, Jun, 2020. "Group decision under uncertain information," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Han, Ying & Song, Zhao & Sun, Jialong & Ma, Jiezhong & Guo, Yangming & Zhu, Peican, 2020. "Investing the effect of age and cooperation in spatial multigame," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    6. You, Tao & Shi, Liang & Wang, Xiaoyu & Mengibaev, Muslimbek & Zhang, Ying & Zhang, Peng, 2021. "The effects of aspiration under multiple strategy updating rules on cooperation in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    7. Wang, Qiuling & Ren, Xiaobin & Gao, Bo & Wang, Jiaqian, 2020. "Heterogeneity reproductive ability promotes cooperation in spatial prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Shi, Juan & Hu, Die & Tao, Rui & Peng, Yunchen & Li, Yong & Liu, Jinzhuo, 2021. "Interaction between populations promotes cooperation in voluntary prisoner's dilemma," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    9. Wang, Chaoqian & Szolnoki, Attila, 2023. "Inertia in spatial public goods games under weak selection," Applied Mathematics and Computation, Elsevier, vol. 449(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. Heiner, Ronald Asher, 2002. "Robust Evolution Of Contingent Cooperation In Pure One-Shot Prisoners' Dilemmas. Part II: Evolutionary Dynamics & Testable Predictions," CSLE Discussion Paper Series 2002-10, Saarland University, CSLE - Center for the Study of Law and Economics.
    2. Niu, Zhenxi & Xu, Jiwei & Dai, Dameng & Liang, Tairan & Mao, Deming & Zhao, Dawei, 2018. "Rational conformity behavior can promote cooperation in the prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 92-96.
    3. Hadzibeganovic, Tarik & Stauffer, Dietrich & Han, Xiao-Pu, 2018. "Interplay between cooperation-enhancing mechanisms in evolutionary games with tag-mediated interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 676-690.
    4. Poulsen, Anders & Svendsen, Gert Tinggaard, 2003. "Rise and Decline of Social Capital," Working Papers 03-10, University of Aarhus, Aarhus School of Business, Department of Economics.
    5. Li, Xiaoyu & Jia, Danyang & Niu, Xiaotong & Liu, Chen & Zhu, Peican & Liu, Dujuan & Chu, Chen, 2022. "Ability-based asymmetrical fitness calculation promotes cooperation in spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Fabrizio Panebianco, 2016. "The role of persuasion in cultural evolution dynamics," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 63(3), pages 233-258, September.
    7. Johan Willner, 2003. "Privatisation and Public Ownership in Finland," CESifo Working Paper Series 1012, CESifo.
    8. Carlo Borzaga & Ermanno Tortia, 2004. "Worker involvement in entrepreneurial nonprofit organizations. Toward a new assessment of workers' perceived satisfaction and fairness," Department of Economics Working Papers 0409, Department of Economics, University of Trento, Italia.
    9. Adrian Bruhin & Ernst Fehr & Daniel Schunk, 2019. "The many Faces of Human Sociality: Uncovering the Distribution and Stability of Social Preferences," Journal of the European Economic Association, European Economic Association, vol. 17(4), pages 1025-1069.
    10. Kimmich, Christian & Fischbacher, Urs, 2016. "Behavioral determinants of supply chain integration and coexistence," Journal of Forest Economics, Elsevier, vol. 25(C), pages 55-77.
    11. Alpizar, Francisco & Carlsson, Fredrik & Johansson-Stenman, Olof, 2005. "How much do we care about absolute versus relative income and consumption?," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 405-421, March.
    12. Engelbert Stockhammer & Paul Ramskogler, 2009. "Post-Keynesian economics How to move forward," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 6(2), pages 227-246.
    13. Scharpf, Fritz W., 2007. "Reflections on multilevel legitimacy," MPIfG Working Paper 07/3, Max Planck Institute for the Study of Societies.
    14. Frank Cowell & Marc Fleurbaey & Bertil Tungodden, 2015. "The tyranny puzzle in social preferences: an empirical investigation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 765-792, December.
    15. Thieme, Lutz & Winkelhake, Olaf & Hartmann, Ulrich, 2014. "Fairness als universelle Norm? Empirische Evidenz ohne Manna [Fairness as a universal norm? Empiric evidence without manna]," Working Papers of the European Institute for Socioeconomics 12, European Institute for Socioeconomics (EIS), Saarbrücken.
    16. Fredrik Carlsson & Olof Johansson‐Stenman & Peter Martinsson, 2007. "Do You Enjoy Having More than Others? Survey Evidence of Positional Goods," Economica, London School of Economics and Political Science, vol. 74(296), pages 586-598, November.
    17. Johnsen, Åshild A & Kvaløy, Ola, 2014. "You always meet twice: An experiment on intrinsic versus instrumental reciprocity," UiS Working Papers in Economics and Finance 2014/2, University of Stavanger.
    18. Ortiz-Riomalo, Juan Felipe & Koessler, Ann-Kathrin & Engel, Stefanie, 2021. "Inducing perspective-taking for prosocial behaviour in natural resource management," Journal of Environmental Economics and Management, Elsevier, vol. 110(C).
    19. Benedikt Herrmann & Henrik Orzen, 2008. "The appearance of homo rivalis: Social preferences and the nature of rent seeking," Discussion Papers 2008-10, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    20. Valeria Maggian & Marie Claire Villeval, 2016. "Social preferences and lying aversion in children," Experimental Economics, Springer;Economic Science Association, vol. 19(3), pages 663-685, September.

    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:509:y:2018:i:c:p:817-826. 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.