IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v56y2013icp53-58.html
   My bibliography  Save this article

The effects of nonlinear imitation probability on the evolution of cooperation

Author

Listed:
  • Dai, Qionglin
  • Li, Haihong
  • Cheng, Hongyan
  • Zhang, Mei
  • Yang, Junzhong

Abstract

In this paper, we introduce a nonlinear imitation rule into an evolutionary prisoner’s dilemma game and investigate how the nonlinear imitation rule affects cooperation. Based on the original version of the proportional imitation rule, the imitation probability for each individual is regulated by a parameter α, which tunes the dependence of the imitation probability on the payoff difference. The results show that there exists an optimal value of α at which the cooperation level reaches its highest value. We carry out the simulations in different types of networks with different mean degrees. Results show that the optimal behavior of cooperation induced by the variation of α is robust. More importantly, from the results we can conclude that there are two crucial factors determining the optimal behavior of cooperation: One is the parameter α, and the other is the regime of payoff difference supporting strong variation of the dependence of the imitation probability on the payoff difference.

Suggested Citation

  • Dai, Qionglin & Li, Haihong & Cheng, Hongyan & Zhang, Mei & Yang, Junzhong, 2013. "The effects of nonlinear imitation probability on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 53-58.
    • Handle: RePEc:eee:chsofr:v:56:y:2013:i:c:p:53-58
    DOI: 10.1016/j.chaos.2013.07.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913001252
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2013.07.001?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. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
    2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    3. Wu, Zhi-Xi & Guan, Jian-Yue & Xu, Xin-Jian & Wang, Ying-Hai, 2007. "Evolutionary prisoner's dilemma game on Barabási–Albert scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 672-680.
    4. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 29-52.
    5. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    6. Flávio L Pinheiro & Jorge M Pacheco & Francisco C Santos, 2012. "From Local to Global Dilemmas in Social Networks," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-6, February.
    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. P. Schimit & B. Santos & C. Soares, 2015. "The evolution of cooperation with different fitness functions using probabilistic cellular automata," Computational Management Science, Springer, vol. 12(1), pages 35-43, January.

    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. Jeromos Vukov & Flávio L Pinheiro & Francisco C Santos & Jorge M Pacheco, 2013. "Reward from Punishment Does Not Emerge at All Costs," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-6, January.
    2. Chengzhang Ma & Wei Cao & Wangheng Liu & Rong Gui & Ya Jia, 2013. "Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    3. Ping Zhu & Guiyi Wei, 2014. "Stochastic Heterogeneous Interaction Promotes Cooperation in Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-10, April.
    4. Ahmadreza Asgharpourmasouleh & Atiye Sadeghi & Ali Yousofi, 2017. "A Grounded Agent-Based Model of Common Good Production in a Residential Complex: Applying Artificial Experiments," SAGE Open, , vol. 7(4), pages 21582440177, October.
    5. Jaime Iranzo & Luis M Floría & Yamir Moreno & Angel Sánchez, 2012. "Empathy Emerges Spontaneously in the Ultimatum Game: Small Groups and Networks," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-8, September.
    6. Giangiacomo Bravo & Lucia Tamburino, 2008. "The Evolution of Trust in Non-Simultaneous Exchange Situations," Rationality and Society, , vol. 20(1), pages 85-113, February.
    7. van den Bergh, Jeroen C.J.M. & Gowdy, John M., 2009. "A group selection perspective on economic behavior, institutions and organizations," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 1-20, October.
    8. Luhe Yang & Duoxing Yang & Lianzhong Zhang, 2022. "The Effect of Bounded Rationality on Human Cooperation with Voluntary Participation," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
    9. Simon Gaechter & Benedikt Herrmann, 2008. "Reciprocity, culture, and human cooperation: Previous insights and a new cross-cultural experiment," Discussion Papers 2008-14, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    10. Wolff, Irenaeus, 2009. "Counterpunishment revisited: an evolutionary approach," MPRA Paper 16923, University Library of Munich, Germany.
    11. Dirk Helbing & Anders Johansson, 2010. "Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-15, October.
    12. Klaus Jaffe & Roberto Cipriani, 2007. "Culture Outsmarts Nature in the Evolution of Cooperation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(1), pages 1-7.
    13. Ahmed, Ali M. & Salas, Osvaldo, 2008. "Is The Hand Of God Involved In Human Cooperation?An Experimental Examination Of The Supernatural Punishment Theory," CAFO Working Papers 2008:1, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.
    14. Konstantin Kurz & Carolin Bock & Michèle Knodt & Anna Stöckl, 2022. "A Friend in Need Is a Friend Indeed? Analysis of the Willingness to Share Self-Produced Electricity During a Long-lasting Power Outage," Schmalenbach Journal of Business Research, Springer, vol. 74(4), pages 727-761, December.
    15. Misato Inaba & Nobuyuki Takahashi, 2019. "Linkage Based on the Kandori Norm Successfully Sustains Cooperation in Social Dilemmas," Games, MDPI, vol. 10(1), pages 1-15, February.
    16. Ding, Rui & Wang, Xianjia & Liu, Yang & Zhao, Jinhua & Gu, Cuiling, 2023. "Evolutionary games with environmental feedbacks under an external incentive mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    17. E Lance Howe & James J Murphy & Drew Gerkey & Colin Thor West, 2016. "Indirect Reciprocity, Resource Sharing, and Environmental Risk: Evidence from Field Experiments in Siberia," PLOS ONE, Public Library of Science, vol. 11(7), pages 1-17, July.
    18. Min, Yong & Du, Yuchen & Jin, Cheng, 2018. "The effect of link rewiring on a coevolutionary common pool resource game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 935-944.
    19. Giulio Cimini, 2017. "Evolutionary Network Games: Equilibria from Imitation and Best Response Dynamics," Complexity, Hindawi, vol. 2017, pages 1-14, August.
    20. Garay, József & Varga, Zoltán, 2011. "Survivor’s dilemma: Defend the group or flee?," Theoretical Population Biology, Elsevier, vol. 80(3), pages 217-225.

    More about this item

    Statistics

    Access and download statistics

    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:56:y:2013:i:c:p:53-58. 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.