Skip to main content
SpringerLink
Log in

Evolutionary dynamics of trust in the N-player trust game with individual reward and punishment

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

Abstract

Trust plays an important role in human society. However, how does trust evolve is a huge challenge. The trust game is a well-known paradigm to measure the evolution of trust in a population. Reward and punishment as the common types of incentives can be used to improve the trustworthiness. However, it remains unclear how reward and punishment actually influence the evolutionary dynamics of trust. Here, we introduce individual reward and punishment into the N-player trust game model in an infinite well-mixed population, where investors use a part of the returned fund to reward trustworthy trustees and meanwhile punish untrustworthy trustees. We then investigate the evolutionary dynamics of trust by means of replicator equations. We show that the introduction of reward and punishment can lead to the stable coexistence state of investors and trustworthy trustees, which indicates that the evolution of trust can be greatly promoted. We reveal that the attraction domain of the coexistence state becomes larger as investors increase the incentive strength from the returned fund for reward and punishment. In addition, we find that the increase of the reward coefficient can enlarge the attraction domain of the coexistence state, which implies that reward can better promote the evolution of trust than punishment.

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

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 that support the results of this study are available from the corresponding authors upon request.]

References

  1. A. Baier, Ethics 96, 231 (1986)

    Article  Google Scholar 

  2. E. Fehr, U. Fischbacher, Nature 425, 785 (2003)

    Article  ADS  Google Scholar 

  3. M.R. Delgado, R.H. Frank, E.A. Phelps, Nat. Neurosci. 8, 1611 (2005)

    Article  Google Scholar 

  4. M. Berens, J. Organ. Chang. Manag. 20, 463 (2007)

    Article  Google Scholar 

  5. E. Petraki, H.A. Abbass, in Proceedings of 7th IEEE Symposium on Computational Intelligence for Security and Defense Applications, Hanoi, Vietnam (2014)

  6. A.W. Brooks, H. Dai, M.E. Schweitzer, Soc. Psychol. Personal. Sci. 5, 467 (2014)

    Article  Google Scholar 

  7. F.S. Grodzinsky, K.W. Miller, M.J. Wolf, Philos. Technol. 28, 91 (2015)

    Article  Google Scholar 

  8. R. Golembiewski, Am. Polit. Sci. Rev. 75, 480 (1981)

    Article  Google Scholar 

  9. S. Knack, P. Keefer, Q. J. Econ. 112, 1251 (1977)

    Article  Google Scholar 

  10. A. Alesina, E.L. Ferrara, J. Pubilc Econ. 85, 207 (2002)

    Article  Google Scholar 

  11. J. Berg, J. Dickhaut, K. McCabe, Games Econ. Behav. 10, 122 (1995)

    Article  Google Scholar 

  12. H.A. Abbass, G. Greenwood, E. Petraki, IEEE Trans. Evol. Comput. 20, 470 (2016)

    Article  Google Scholar 

  13. G. Charness, N. Du, C. Yang, Games Econ. Behav. 72, 361 (2011)

    Article  Google Scholar 

  14. M. Chica, R. Chiong, M. Kirley, H.A. Ishibuchi, IEEE Trans. Evol. Comput. 22, 866 (2018)

    Article  Google Scholar 

  15. M. Chica, R. Chiong, J. Ramasco, H.A. Abbass, Commun. Nonlinear Sci. Numer. Simul. 79, 104870 (2019)

    Article  MathSciNet  Google Scholar 

  16. I.S. Lim, Phys. Rev. E 102, 062419 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  17. K. Sigmund, Trends Ecol. Evol. 22, 593 (2007)

    Article  Google Scholar 

  18. A. Szolnoki, M. Perc, EPL 92, 38003 (2010)

    Article  ADS  Google Scholar 

  19. A. Szolnoki, G. Szabó, M. Perc, Phys. Rev. E 83, 036101 (2011)

    Article  ADS  Google Scholar 

  20. A. Szolnoki, M. Perc, New J. Phys. 14, 093016 (2012)

    Article  ADS  Google Scholar 

  21. M. Perc, Sci. Rep. 2, 344 (2012)

    Article  ADS  Google Scholar 

  22. N.J. Raihani, A. Thornton, R. Bshary, Trends Ecol. Evol. 27, 288 (2012)

    Article  Google Scholar 

  23. A. Szolnoki, M. Perc, Phys. Rev. X 3, 041021 (2013)

    Google Scholar 

  24. X. Chen, A. Szolnoki, M. Perc, New J. Phys. 16, 083016 (2014)

    Article  MathSciNet  ADS  Google Scholar 

  25. K. Li, R. Cong, T. Wu, L. Wang, Phys. Rev. E 91, 042810 (2015)

    Article  ADS  Google Scholar 

  26. C. Wang, L. Wang, J. Wang, S. Sun, C. Xia, Appl. Math. Comput. 293, 18 (2017)

    MathSciNet  Google Scholar 

  27. M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki, Phys. Rep. 687, 1 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  28. C. Du, D. Jia, L. Jin, L. Shi, Eur. Phys. J. B 91, 234 (2018)

    Article  ADS  Google Scholar 

  29. J. Riehl, P. Ramazi, M. Cao, Annu. Rev. Control 45, 87 (2018)

    Article  MathSciNet  Google Scholar 

  30. L. Liu, S. Wang, X. Chen, M. Perc, Chaos 28, 103105 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  31. T.A. Han, L.T. Thanh, Sci. Rep. 8, 15997 (2018)

    Article  ADS  Google Scholar 

  32. T. Chen, X. Hu, Y. Wang, L. Wang, Eur. Phys. J. B 91, 112 (2018)

    Article  ADS  Google Scholar 

  33. Y. Zhang, F. Fu, PLOS One 13, 5 (2018)

    Google Scholar 

  34. Y. Zhang, X. Chen, A. Liu, C. Sun, Appl. Math. Comput. 321, 641 (2018)

    MathSciNet  Google Scholar 

  35. L. Ratliff, R. Dong, S. Sekar, T. Fiez, Annu. Rev. Control Robot. Auton. Syst. 2, 305 (2019)

    Article  Google Scholar 

  36. X. Li, H. Wang, C. Xia, M. Perc, Front. Phys. 7, 125 (2019)

    Article  Google Scholar 

  37. Y. Zhang, J. Liu, A. Li, Complexity 2019, 2915020 (2019)

    Google Scholar 

  38. Y. Fang, T.P. Benko, M. Perc, H. Xu, Q. Tan, Proc. R. Soc. A. 475, 20190349 (2019)

    Article  ADS  Google Scholar 

  39. L. Hu, N. He, Q. Weng, X. Chen, M. Perc, Chaos Soliton. Fract 134, 109694 (2020)

    Article  Google Scholar 

  40. Q. Chang, Y. Zhang, Eur. Phys. J. B 94, 100 (2021)

    Article  ADS  Google Scholar 

  41. M. Rigdon, J. Econ. Behav. Organ. 70, 93 (2009)

    Article  Google Scholar 

  42. H. Sun, M. Bigoni, J. Behav. Exp. Econ. 77, 158 (2018)

    Article  Google Scholar 

  43. X. Pan, D. Houser, J. Econ. Behav. Organ. 158, 236 (2019)

    Article  Google Scholar 

  44. J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  45. M.A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, Harvard, 2006)

    Book  MATH  Google Scholar 

  46. K. Sigmund, The Calculus of Selfishness (Princeton University Press, Princeton, 2010)

    Book  MATH  Google Scholar 

  47. W.H. Sandholm, Population Games and Evolutionary Dynamics (MIT Press, London, 2010)

    MATH  Google Scholar 

  48. T. Sasaki, Å. Brännström, U. Dieckmann, K. Sigmund, Proc. Natl. Acad. Sci. USA 109, 1165 (2012)

    Article  ADS  Google Scholar 

  49. F. Huang, X. Chen, L. Wang, J. Theor. Biol. 449, 60 (2018)

    Article  ADS  Google Scholar 

  50. C. Hauert, N. Haiden, K. Sigmund, Discret. Contin. Dyn. Syst. Ser. B. 4, 575 (2004)

    Google Scholar 

  51. C. Hauert, A. Traulsen, H. De Silva née Brandt, M.A. Nowak, K. Sigmund, Biol. Theor. 3, 114 (2008)

  52. T. Sasaki, S. Uchida, Proc. R. Soc. B. 280, 20122498 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 61976048, 62036002) and the Fundamental Research Funds of the Central Universities of China.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Xing Fang & Xiaojie Chen

Authors
  1. Xing Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaojie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

XC and XF designed the research, XF performed the research, and XF and XC wrote the manuscript.

Corresponding author

Correspondence to Xiaojie Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, X., Chen, X. Evolutionary dynamics of trust in the N-player trust game with individual reward and punishment. Eur. Phys. J. B 94, 176 (2021). https://doi.org/10.1140/epjb/s10051-021-00185-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00185-w

Search

Navigation