Skip to main content
SpringerLink
Log in

Reputational preference-based payoff punishment promotes cooperation in spatial social dilemmas

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

To explore the incentive mechanisms of cooperation in social dilemmas. Motivated by preference for reputation in indirect reciprocity, we propose a reputational preference-based payoff punishment mechanism, under which an individual is punished if his reputation is lower than the average one of direct neighbors and his current game strategy is defection. The cost of punishment is shared by the immediate neighbors. Simulation results show that in spatial prisoner’s dilemma game and snowdrift game, the punishment mechanism reduces the fitness of both cooperators and defectors in the micro-perspective, whereas it significantly promotes the evolution of cooperation from the macro view. Furthermore, it is easier for cooperation to emerge and sustain in snowdrift game, and compared to prisoner’s dilemma game, within the most range of model parameters, the system is in the coexistence state of cooperators and defectors.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data used to support the findings of this study are available from the corresponding author upon request.]

References

  1. E. Pennisi, How did cooperative behavior evolve? Science 309, 93 (2005)

    Article  Google Scholar 

  2. S.J. Gould, Darwinism and the expansion of evolutionary theory. Science 216, 380–387 (1982)

    Article  ADS  Google Scholar 

  3. C. Hilbe, T. Röhl, M. Milinski, Extortion subdues human players but is finally punished in the prisoner’s dilemma. Nat. Commun 5, 1–6 (2014)

    Article  Google Scholar 

  4. M.A. Nowak, A. Sasaki, C. Taylor et al., Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)

    Article  ADS  Google Scholar 

  5. J.E. Bone, B. Wallace, R. Bshary et al., Power asymmetries and punishment in a prisoner’s dilemma with variable cooperative investment. PloS one 11, e0155773 (2016)

    Article  Google Scholar 

  6. X. Deng, Q. Zhang, Y. Deng et al., A novel framework of classical and quantum prisoner’s dilemma games on coupled networks. Sci. Rep. 6, 1–11 (2016)

    Google Scholar 

  7. J.M. Smith, In Evolution and the Theory of Games (Cambridge University Press, Cambridge, 1982)

    Book  Google Scholar 

  8. J.W. Weibull, In Evolutionary Game Theory (MIT press, Cambridge, 1997)

    Google Scholar 

  9. H. Gintis, In Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Behavior (Princeton University Press, Princeton, 2000)

    MATH  Google Scholar 

  10. M.W. Macy, A. Flache, Learning dynamics in social dilemmas. Proc. Natl. Acad. Sci. USA 99, 7229–7236 (2002)

    Article  ADS  MATH  Google Scholar 

  11. F.C. Santos, J.M. Pacheco, T. Lenaerts, Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl. Acad. Sci. U.S.A. 103, 3490–3494 (2006)

    Article  ADS  Google Scholar 

  12. A. Szolnoki, M. Perc, Resolving social dilemmas on evolving random networks. EPL 86, 30007 (2009)

    Article  ADS  Google Scholar 

  13. M.G. Zimmermann, V.M. Eguluz, Cooperation, social networks, and the emergence of leadership in a prisoner’s dilemma with adaptive local interactions. Phys. Rev. E 72, 056118 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Szolnoki, G. Szab, Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner’s Dilemma games. EPL 77, 30004 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Perc, A. Szolnoki, Social diversity and promotion of cooperation in the spatial prisoner’s dilemma game. Phys. Rev. E 77, 011904 (2008)

    Article  ADS  Google Scholar 

  16. C. Hauert, M. Doebeli, Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428, 643–646 (2004)

    Article  ADS  Google Scholar 

  17. W. Du, X. Cao, M. Hu et al., Asymmetric cost in snowdrift game on scale-free networks. EPL 87, 60004 (2009)

    Article  ADS  Google Scholar 

  18. M.O. Souza, J.M. Pacheco, F.C. Santos, Evolution of cooperation under N-person snowdrift games. J. Theor. Biol. 260, 581–588 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. M. Sefton, R. Shupp, J.M. Walker, The effect of rewards and sanctions in provision of public goods. Econ Inq 45, 671–690 (2007)

    Article  Google Scholar 

  20. D.G. Rand, A. Dreber, T. Ellingsen et al., Positive interactions promote public cooperation. Science 325, 1272–1275 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. A. Szolnoki, M. Perc, Reward and cooperation in the spatial public goods game. EPL 92, 38003 (2010)

    Article  ADS  Google Scholar 

  22. M.A. Nowak, Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006)

    Article  ADS  Google Scholar 

  23. M. Milinski, D. Semmann, H.J. Krambeck, Reputation helps solve the ‘tragedy of the commons’. Nature 415, 424–426 (2002)

    Article  ADS  Google Scholar 

  24. C. Wedekind, V.A. Braithwaite, The long-term benefits of human generosity in indirect reciprocity. Curr. Biol. 12, 1012–1015 (2002)

    Article  Google Scholar 

  25. P. Barclay, Trustworthiness and competitive altruism can also solve the ‘tragedy of the commons’. Evol. Hum. Behav. 25, 209–220 (2004)

    Article  Google Scholar 

  26. F. Fu, C. Hauert, M.A. Nowak et al., Reputation-based partner choice promotes cooperation in social networks. Phys. Rev. E 78, 026117 (2008)

    Article  ADS  Google Scholar 

  27. M.A. Nowak, M.M. Robert, Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)

    Article  ADS  Google Scholar 

  28. E. Lieberman, C. Hauert, M.A. Nowak, Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)

    Article  ADS  Google Scholar 

  29. P. Holme, B.J. Kim, Growing scale-free networks with tunable clustering. Phys. Rev. E 65, 026107 (2002)

    Article  ADS  Google Scholar 

  30. F.C. Santos, J.M. Pacheco, Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95, 098104 (2005)

    Article  ADS  Google Scholar 

  31. A. Szolnoki, M. Perc, Z. Danku, Towards effective payoffs in the prisoner’s dilemma game on scale-free networks. Physica A 387, 2075–2082 (2008)

    Article  ADS  Google Scholar 

  32. N. Masuda, K. Aihara, Spatial prisoner’s dilemma optimally played in small-world networks. Phys. Lett. A 313, 55–61 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. G. Szab, J. Vukov, Cooperation for volunteering and partially random partnerships. Phys. Rev. E 69, 036107 (2004)

    Article  ADS  Google Scholar 

  34. X. Chen, L. Wang, Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. Phys. Rev. E 77, 017103 (2008)

    Article  ADS  Google Scholar 

  35. R. Axelrod, An evolutionary approach to norms. Am. Polit Sci. Rev. 80, 1095–1111 (1986)

    Article  Google Scholar 

  36. E. Ostrom, J. Walker, R. Gardner, Covenants with and without a sword: self-governance is possible. Am. Polit Sci. Rev. 86, 404–417 (1992)

    Article  Google Scholar 

  37. E. Fehr, S. Gächter, Cooperation and punishment in public goods experiments. Am. Econ. Rev. 90, 980–994 (2000)

    Article  Google Scholar 

  38. E. Fehr, S. Gächter, Altruistic punishment in humans. Nature 415, 137–140 (2002)

  39. D. Masclet, C. Noussair, S. Tucker et al., Monetary and nonmonetary punishment in the voluntary contributions mechanism. Am. Econ. Rev. 93, 366–380 (2003)

    Article  Google Scholar 

  40. J. Andreoni, W. Harbaugh, L. Vesterlund, The carrot or the stick: rewards, punishments, and cooperation. Am. Econ. Rev. 93, 893–902 (2003)

    Article  Google Scholar 

  41. D. Helbing, A. Szolnoki, M. Perc et al., Punish, but not too hard: how costly punishment spreads in the spatial public goods game. New J. Phys. 12, 083005 (2010)

    Article  ADS  Google Scholar 

  42. Z. Wang, C. Xia, S. Meloni et al., Impact of social punishment on cooperative behavior in complex networks. Sci. Rep. 3, 3055 (2013)

  43. A. Szolnoki, G. Szab, M. Perc, Phase diagrams for the spatial public goods game with pool punishment. Phys. Rev. E 83, 036101 (2011)

    Article  ADS  Google Scholar 

  44. A. Szolnoki, G. Szab, L. Czak, Competition of individual and institutional punishments in spatial public goods games. Phys. Rev. E 046106(2011)

  45. A. Szolnoki, M. Perc, Effectiveness of conditional punishment for the evolution of public cooperation. J. Theor. Biol. 325, 34–41 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. X. Chen, A. Szolnoki, M. Perc, Probabilistic sharing solves the problem of costly punishment. New J. Phys. 16, 083016 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  47. M. Perc, A. Szolnoki, A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games. Sci. Rep. 5, 1–11 (2015)

    Article  Google Scholar 

  48. X. Chen, A. Szolnoki, Punishment and inspection for governing the commons in a feedback-evolving game. PLoS Comput. Biol. 14, e1006347 (2018)

    Article  ADS  Google Scholar 

  49. A. Szolnoki, M. Perc, Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment. Phys. Rev. X 7, 041027 (2017)

    Google Scholar 

  50. G. Szab, C. Tke, Evolutionary prisoner’s dilemma game on a square lattice. Phys. Rev. E 58, 69 (1998)

    Article  ADS  Google Scholar 

  51. M.A. Nowak, R.M. May, The spatial dilemmas of evolution. Int. J. Bifurcat. Chaos 3, 35–78 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by (i) Research on Complex Network Hogher-order Structure-based Key Community and Node Discovery, as well as Power Network Planning and Security; (ii) National Natural Science Foundation of China (Grant No. 62062049); (iii) Project supported by the Natural Science Foundation of Gansu Province, China (Grant No. 20JR5RA390).

Author information

Authors and Affiliations

  1. State Grid Gansu Information and Telecommunication Company, Lanzhou, 730050, China

    Xiang Wei, Peng Xu & Shuiting Du

  2. School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Guanghui Yan & Huayan Pei

Authors
  1. Xiang Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuiting Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guanghui Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huayan Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization, XW; methodology, PX and S-TD; software, XW and G-HY; validation, S-TD and H-YP; writing-original draft, XW; writing-review and editing, H-YP and PX. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Huayan Pei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, X., Xu, P., Du, S. et al. Reputational preference-based payoff punishment promotes cooperation in spatial social dilemmas. Eur. Phys. J. B 94, 210 (2021). https://doi.org/10.1140/epjb/s10051-021-00212-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00212-w

Search

Navigation