Advertisement

Evolutionary dynamics of cooperation in the public goods game with pool exclusion strategies

  • Linjie Liu
  • Xiaojie ChenEmail author
  • Matjaž Perc
Original Paper
  • 163 Downloads

Abstract

Social exclusion is widely used as a control mechanism to promote cooperative behavior in human societies. However, it remains unclear how such control strategies actually influence the evolutionary dynamics of cooperation. In this paper, we introduce two types of control strategies into a population of agents that play the public goods game, namely prosocial pool exclusion and antisocial pool exclusion, and we use the replicator equation to study the resulting evolutionary dynamics for infinite well-mixed populations. We show that the introduction of prosocial pool exclusion can stabilize the coexistence of cooperators and defectors by means of periodic oscillations, but only in the absence of second-order prosocial pool exclusion. When considering also antisocial pool exclusion, we show that the population exhibits a heteroclinic circle, where cooperators can coexist with other strategists. Moreover, when second-order exclusion is taken into account, we find that prosocial pool exclusion is the dominant strategy, regardless of whether the second-order exclusion is prosocial or antisocial. In comparison with punishment, we conclude that prosocial pool exclusion is a more effective control mechanism to curb free-riding.

Keywords

Evolutionary dynamics of cooperation Pool exclusion Public goods game Replicator equation 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 61503062) and by the Slovenian Research Agency (Grant Nos. J1-7009, J4-9302, J1-9112 and P1-0403).

Compliance with ethical standards

Conflict of interest

The authors declare that no competing interest exist.

References

  1. 1.
    Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  2. 2.
    Hofbauer, J., Sigmund, K.: Evolutionary game dynamics. B. Am. Math. Soc. 40(4), 479–519 (2003)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Perc, M., Szolnoki, A., Szabó, G.: Restricted connections among distinguished players support cooperation. Phys. Rev. E 78(6), 066101 (2008)Google Scholar
  4. 4.
    Perc, M., Szolnoki, A.: Coevolutionary games—a mini review. BioSystems 99(2), 109–125 (2010)Google Scholar
  5. 5.
    Xia, C., Wang, L., Sun, S., Wang, J.: An SIR model with infection delay and propagation vector in complex networks. Nonlinear Dyn. 69(3), 927–934 (2012)MathSciNetGoogle Scholar
  6. 6.
    Xia, C., Miao, Q., Wang, J., Ding, S.: Evolution of cooperation in the traveler’s dilemma game on two coupled lattices. Appl. Math. Comput. 246, 389–398 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Javarone, M.A.: Statistical physics of the spatial Prisoner’s dilemma with memory-aware agents. Eur. Phys. J. B 89(2), 1 (2016)MathSciNetGoogle Scholar
  8. 8.
    Amaral, M.A., Wardil, L., Perc, M., da Silva, J.K.: Stochastic win-stay-lose-shift strategy with dynamic aspirations in evolutionary social dilemmas. Phys. Rev. E 94(3), 032317 (2016)Google Scholar
  9. 9.
    Riehl, J.R., Cao, M.: Towards optimal control of evolutionary games on networks. IEEE Trans. Automat. Cont. 62(1), 458–462 (2017)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Ma, J., Zheng, Y., Wang, L.: Nash equilibrium topology of multi-agent systems with competitive groups. IEEE Trans. Ind. Electron. 64(6), 4956–4966 (2017)Google Scholar
  11. 11.
    Amaral, M.A., Javarone, M.A.: Heterogeneous update mechanisms in evolutionary games: mixing innovative and imitative dynamics. Phys. Rev. E 97(4), 042305 (2018)Google Scholar
  12. 12.
    Javarone, M.A.: The Host-Pathogen game: an evolutionary approach to biological competitions. Front. Phys. 6, 94 (2018)Google Scholar
  13. 13.
    He, N., Chen, X., Szolnoki, A.: Central governance based on monitoring and reporting solves the collective-risk social dilemma. Appl. Math. Comput. 347, 334–341 (2019)MathSciNetGoogle Scholar
  14. 14.
    Chen, X., Brännström, Å., Dieckmann, U.: Parent-preferred dispersal promotes cooperation in structured populations. Proc. R. Soc. B 286(1895), 20181949 (2019)Google Scholar
  15. 15.
    Santos, F.C., Pacheco, J.M.: Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95(9), 098104 (2005)Google Scholar
  16. 16.
    Tanimoto, J., Sagara, H.: Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game. BioSystems 90(1), 105–114 (2007)Google Scholar
  17. 17.
    Tanimoto, J.: Promotion of cooperation by payoff noise in a \(2\times 2\) game. Phys. Rev. E 76(4), 041130 (2007)MathSciNetGoogle Scholar
  18. 18.
    Santos, F.C., Santos, M.D., Pacheco, J.M.: Social diversity promotes the emergence of cooperation in public goods games. Nature 454(7201), 213 (2008)Google Scholar
  19. 19.
    Szolnoki, A., Perc, M.: Coevolution of teaching activity promotes cooperation. New J. Phys. 10(4), 043036 (2008)Google Scholar
  20. 20.
    Santos, F.C., Francisco, C., Pacheco, J.M.: Risk of collective failure provides an escape from the tragedy of the commons. Proc. Natl. Acad. Sci. USA 108(26), 10421–10425 (2011)Google Scholar
  21. 21.
    Sasaki, T., Brännström, A., Dieckmann, U., Sigmund, K.: The take-it-or-leave-it option allows small penalties to overcome social dilemmas. Proc. Natl. Acad. Sci. USA 109(4), 1165–1169 (2012)zbMATHGoogle Scholar
  22. 22.
    Xia, C., Wang, J., Wang, L., Sun, S., Sun, J., Wang, J.: Role of update dynamics in the collective cooperation on the spatial snowdrift games: beyond unconditional imitation and replicator dynamics. Chaos Solitons Fract. 45(9–10), 1239–1245 (2012)MathSciNetGoogle Scholar
  23. 23.
    Wang, C., Wang, L., Wang, J., Sun, S., Xia, C.: Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices. Appl. Math. Comput. 293, 18–29 (2017)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Perc, M., Jordan, J.J., Rand, D.G., Wang, Z., Boccaletti, S., Szolnoki, A.: Statistical physics of human cooperation. Phys. Rep. 687, 1–51 (2017)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Shi, L., Shen, C., Geng, Y., Chu, C., Meng, H., Perc, M., Boccaletti, S., Wang, Z.: Winner-weaken-loser-strengthen rule leads to optimally cooperative interdependent networks. Nonlinear Dyn. 96(1), 49–56 (2019)Google Scholar
  26. 26.
    Nowak, M.A., Sigmund, K.: The dynamics of indirect reciprocity. J. Theor. Biol. 194(4), 561–574 (1998)Google Scholar
  27. 27.
    Clutton-Brock, T.: Breeding together: kin selection and mutualism in cooperative vertebrates. Science 296(5565), 69–72 (2002)Google Scholar
  28. 28.
    Fu, F., Hauert, C., Nowak, M.A., Wang, L.: Reputation-based partner choice promotes cooperation in social networks. Phys. Rev. E 78(2), 026117 (2008)Google Scholar
  29. 29.
    Hauert, C.: Replicator dynamics of reward reputation in public goods games. J. Theor. Biol. 267(1), 22–28 (2010)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Tanimoto, J., Brede, M., Yamauchi, A.: Network reciprocity by coexisting learning and teaching strategies. Phys. Rev. E 85(3), 032101 (2012)Google Scholar
  31. 31.
    Chen, X., Szolnoki, A., Perc, M.: Competition and cooperation among different punishing strategies in the spatial public goods game. Phys. Rev. E 92(1), 012819 (2015)MathSciNetGoogle Scholar
  32. 32.
    Szolnoki, A., Perc, M.: Antisocial pool rewarding does not deter public cooperation. Proc. R. Soc. B 282(1816), 20151975 (2015)Google Scholar
  33. 33.
    Chen, M., Wang, L., Sun, S., Wang, J., Xia, C.: Evolution of cooperation in the spatial public goods game with adaptive reputation assortment. Phys. Lett. A 380(1–2), 40–47 (2016)zbMATHGoogle Scholar
  34. 34.
    Szolnoki, A., Perc, M.: Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment. Phys. Rev. X 7(4), 041027 (2017)Google Scholar
  35. 35.
    Chen, X., Szolnoki, A.: Punishment and inspection for governing the commons in a feedback-evolving game. PLoS Comput. Biol. 14(7), e1006347 (2018)Google Scholar
  36. 36.
    Su, Q., Li, A., Wang, L., Eugene Stanley, H.: Spatial reciprocity in the evolution of cooperation. Proc. R. Soc. B 286(1900), 20190041 (2019)Google Scholar
  37. 37.
    Fehr, E., Gächter, S.: Cooperation and punishment in public goods experiments. Am. Econ. Rev. 90(90), 980–994 (2000)Google Scholar
  38. 38.
    Boyd, R., Gintis, H., Bowles, S., Richerson, P.J.: The evolution of altruistic punishment. Proc. Natl. Acad. Sci. USA 100(6), 3531–3535 (2003)Google Scholar
  39. 39.
    Szolnoki, A., Szabó, G., Czakó, L.: Competition of individual and institutional punishments in spatial public goods games. Phys. Rev. E 84(4), 046106 (2011)Google Scholar
  40. 40.
    Perc, M.: Sustainable institutionalized punishment requires elimination of second-order free-riders. Sci. Rep. 2, 344 (2012)Google Scholar
  41. 41.
    Vasconcelos, V.V., Santos, F.C., Pacheco, J.M.: A bottom-up institutional approach to cooperative governance of risky commons. Nat. Clim. Change 3(9), 797 (2013)Google Scholar
  42. 42.
    Chen, X., Szolnoki, A., Perc, M.: Probabilistic sharing solves the problem of costly punishment. New J. Phys. 16(8), 083016 (2014)MathSciNetGoogle Scholar
  43. 43.
    Wu, J.J., Zhang, B., Zhou, Z., He, Q.Q., Zheng, X., Cressman, R., Tao, Y.: Costly punishment does not always increase cooperation. Proc. Natl. Acad. Sci. USA 106(41), 17448–17451 (2009)Google Scholar
  44. 44.
    Baumard, N.: Has punishment played a role in the evolution of cooperation? A critical review. Mind Soc. 9(2), 171–192 (2010)Google Scholar
  45. 45.
    Hauser, O.P., Nowak, M.A., Rand, D.G.: Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible. J. Theor. Biol. 360(25), 163–171 (2014)zbMATHGoogle Scholar
  46. 46.
    Dreber, A., Rand, D.G.: Retaliation and antisocial punishment are overlooked in many theoretical models as well as behavioral experiments. Behav. Brain Sci. 35(1), 24–24 (2012)Google Scholar
  47. 47.
    Irwin, K., Horne, C.: A normative explanation of antisocial punishment. Soc. Sci. Res. 42(2), 562–570 (2013)Google Scholar
  48. 48.
    Rand, D.G., Armao IV, J.J., Nakamaru, M., Ohtsuki, H.: Anti-social punishment can prevent the co-evolution of punishment and cooperation. J. Theor. Biol. 265(4), 624–632 (2010)MathSciNetGoogle Scholar
  49. 49.
    Rand, D.G., Nowak, M.A.: The evolution of anti-social punishment in optional public goods games. Nat. Commun. 2, 434 (2011)Google Scholar
  50. 50.
    Ouwerkerk, J.W., Kerr, N.L., Gallucci, M., Van Lange, P.M.: Avoiding the social death penalty: ostracism and cooperation in social dilemmas. In: Williams, K.D., Forgas, J.P., von Hippel, W. (eds.) The Social Outcast: Ostracism, Social Exclusion, Rejection, and Bullying, pp. 321–332. Psychology Press, New York (2005)Google Scholar
  51. 51.
    Sasaki, T., Uchida, S.: The evolution of cooperation by social exclusion. Proc. R. Soc. B 280(1752), 20122498 (2012)Google Scholar
  52. 52.
    Li, K., Cong, R., Wu, T., Wang, L.: Social exclusion in finite populations. Phys. Rev. E 91(4), 042810 (2015)Google Scholar
  53. 53.
    Liu, L., Chen, X., Szolnoki, A.: Competitions between prosocial exclusions and punishments in finite populations. Sci. Rep. 7, 46634 (2017)Google Scholar
  54. 54.
    Szolnoki, A., Chen, X.: Alliance formation with exclusion in the spatial public goods game. Phys. Rev. E 95(5), 052316 (2017)Google Scholar
  55. 55.
    Liu, L., Wang, S., Chen, X., Perc, M.: Evolutionary dynamics in the public goods games with switching between punishment and exclusion. Chaos 28(10), 103105 (2018)MathSciNetzbMATHGoogle Scholar
  56. 56.
    Sigmund, K., Silva, D.H., Traulsen, A., Hauert, C.: Social learning promotes institutions for governing the commons. Nature 466(7308), 861–863 (2010)Google Scholar
  57. 57.
    Twenge, J.M., Baumeister, R.F., DeWall, C.N., Ciarocco, N.J., Bartels, J.M.: Social exclusion decreases prosocial behavior. J. Pers. Soc. Psychol. 92(1), 56 (2007)Google Scholar
  58. 58.
    Bernstein, M.J., Young, S.G., Brown, C.M., Sacco, D.F., Claypool, H.M.: Adaptive responses to social exclusion: social rejection improves detection of real and fake smiles. Psychol. Sci. 19(10), 981–983 (2008)Google Scholar
  59. 59.
    Carter-Sowell, A.R., Chen, Z., Williams, K.D.: Ostracism increases social susceptibility. Soc. Influ. 3(3), 143–153 (2008)Google Scholar
  60. 60.
    Pollatos, O., Matthias, E., Keller, J.: When interoception helps to overcome negative feelings caused by social exclusion. Front. Psychol. 6, 786 (2015)Google Scholar
  61. 61.
    Schuster, P., Sigmund, K.: Replicator dynamics. J. Theor. Biol. 100(3), 533–538 (1983)MathSciNetGoogle Scholar
  62. 62.
    Hauert, C., De, M.S., Hofbauer, J., Sigmund, K.: Replicator dynamics for optional public good games. J. Theor. Biol. 218(2), 187–194 (2002)MathSciNetGoogle Scholar
  63. 63.
    Nowak, M.A., Sigmund, K.: Evolutionary dynamics of biological games. Science 303(5659), 793–799 (2004)Google Scholar
  64. 64.
    Szolnoki, A., Chen, X.: Benefits of tolerance in public goods games. Phys. Rev. E 92(4), 042813 (2015)Google Scholar
  65. 65.
    Weitz, J.S., Eksin, C., Paarporn, K., Brown, S.P., Ratcliff, W.C.: An oscillating tragedy of the commons in replicator dynamics with game-environment feedback. Proc. Natl. Acad. Sci. USA 113(47), E7518–E7525 (2016)Google Scholar
  66. 66.
    Wang, Q., He, N., Chen, X.: Replicator dynamics for public goods game with resource allocation in large populations. Appl. Math. Comput. 328, 162–170 (2018)MathSciNetGoogle Scholar
  67. 67.
    Sasaki, T., Unemi, T.: Replicator dynamics in public goods games with reward funds. J. Theor. Biol. 287(1), 109–114 (2011)MathSciNetzbMATHGoogle Scholar
  68. 68.
    Szolnoki, A., Perc, M., Szabó, G.: Phase diagrams for three-strategy evolutionary prisoner’s dilemma games on regular graphs. Phys. Rev. E 80(5), 056104 (2009)Google Scholar
  69. 69.
    Wang, Z., Xu, B., Zhou, H.J.: Social cycling and conditional responses in the Rock–Paper–Scissors game. Sci. Rep. 4, 5830 (2014)Google Scholar
  70. 70.
    Sigmund, K., Hauert, C., Traulsen, A., Silva, D.H.: Social control and the social contract: the emergence of sanctioning systems for collective action. Dyn. Games Appl. 1(1), 149–171 (2011)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  3. 3.Center for Applied Mathematics and Theoretical PhysicsUniversity of MariborMariborSlovenia
  4. 4.Complexity Science Hub ViennaViennaAustria

Personalised recommendations