From defection to ingroup favoritism to cooperation: simulation analysis of the social dilemma in dynamic networks

Abstract

The emergence of cooperation in social dilemmas is a core question in the social sciences, the proposed solution being ingroup favoritism, a conditional strategy where individuals only cooperate with members of their own group. However, empirical literature has suggested that ingroup favoritism prevents one from realizing profitable interactions with outgroup members. Such an observation calls for a theoretical analysis that would help in understanding what factors affect the transition from ingroup favoritism to unconditional cooperation. Here, we conducted computational experiments in which agents located in social networks imitate traits of successful neighbors or sever social ties with defecting neighbors and connect them to other agents. The results of our simulation showed transitions from unconditional defection to ingroup favoritism to unconditional cooperation with a more frequent occurrence of link rewiring. This indicates the usefulness of the dynamic-networks framework in understanding the reason why cooperation is achieved in specific societies and why different types of cooperation are observed in different ones.

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Notes

  1. 1.

    Because cooperation with ingroup members was presumed in this study, this rule was similar to the assumption that agents cut relationships with outgroup members.

  2. 2.

    In [34], the dissimilarity between agents i and j (\(d_{ij}\)) is calculated by the two agents’ tags. Agent i compares this dissimilarity with his/her tolerance level (\(t_i\)) and chooses cooperation if the neighbor (j) is sufficiently similar (i.e., \(d_{ij} < t_{i}\)). The focal agent cuts the link to his/her neighbor if he/she chooses defection (i.e., \(d_{ij} \ge t_i\)).

  3. 3.

    In [34], a link forms between the focal agent (i) and a potential new neighbor (n) if \(d_{in} < t_{i}\) and \(d_{in} < t_{n}\). This notation mimics that of footnote 2.

  4. 4.

    The replication material of the simulation will be available on the author’s web page.

  5. 5.

    We computed the effective number of tags in the population as the index of tag diversity (see [36], for this index). Specifically, I computed \(1/\sum _{g} p_g^2\), where \(p_g\) is the proportion of agents who adopt tag g. For example, this index takes the value of n when the population is occupied by n equal-sized groups.

References

  1. 1.

    Adams, G. (2005). The cultural grounding of personal relationship: Enemyship in North American and West African worlds. Journal of Personality and Social Psychology, 88(6), 948–968.

    Article  Google Scholar 

  2. 2.

    Alesina, A., Baqir, R., & Easterly, W. (1999). Public goods and ethnic divisions. The Quarterly Journal of Economics, 114(4), 1243–1284.

    Article  Google Scholar 

  3. 3.

    Algan, Y., Hémet, C., & Laitin, D. D. (2016). The social effects of ethnic diversity at the local level: A natural experiment with exogenous residential allocation. Journal of Political Economy, 124(3), 696–733.

    Article  Google Scholar 

  4. 4.

    Antonioni, A., Sánchez, A., & Tomassini, M. (2016). Cooperation survives and cheating pays in a dynamic network structure with unreliable reputation. Scientific Reports, 6(May), 27160.

    Article  Google Scholar 

  5. 5.

    Apicella, C. L., Marlowe, F. W., Fowler, J. H., & Christakis, N. A. (2012). Social networks and cooperation in hunter-gatherers. Nature, 481(7382), 497–501.

    Article  Google Scholar 

  6. 6.

    Axelrod, R. (1984). The evolution of cooperation 1984. New York: Basic Books.

    Google Scholar 

  7. 7.

    Axelrod, R. (1997). The dissemination of culture: A model with local convergence and global polarization. Journal of Conflict Resolution, 41(2), 203–226.

    Article  Google Scholar 

  8. 8.

    Bernhard, H., Fischbacher, U., & Fehr, E. (2006). Parochial altruism in humans. Nature, 442(7105), 912–915.

    Article  Google Scholar 

  9. 9.

    Bond, R. M., Fariss, C. J., Jones, J. J., Kramer, A. D. I., Marlow, C., Settle, J. E., et al. (2012). A 61-million-person experiment in social influence and political mobilization. Nature, 489(7415), 295–298.

    Article  Google Scholar 

  10. 10.

    Centola, D., Gonzalez-Avella, J. C., Eguíluz, V. M., & San Miguel, M. (2007). Homophily, cultural drift, and the co-evolution of cultural groups. Journal of Conflict Resolution, 51(6), 905–929.

    Article  Google Scholar 

  11. 11.

    Centola, D., & Macy, M. (2007). Complex contagions and the weakness of long ties. American Journal of Sociology, 113(3), 702–734.

    Article  Google Scholar 

  12. 12.

    Christakis, N. A., & Fowler, J. H. (2009). Connected: The surprising power of our social networks and how they shape our lives. New York: Little, Brown & Company.

    Google Scholar 

  13. 13.

    Cuesta, J. A., Gracia-Lázaro, C., Ferrer, A., Moreno, Y., & Sánchez, A. (2015). Reputation drives cooperative behaviour and network formation in human groups. Scientific Reports, 5(1), 7843.

    Article  Google Scholar 

  14. 14.

    Diekmann, A., Jann, B., Przepiorka, W., & Wehrli, S. (2014). Reputation formation and the evolution of cooperation in anonymous online markets. American Sociological Review, 79(1), 65–85.

    Article  Google Scholar 

  15. 15.

    Efferson, C., Lalive, R., & Fehr, E. (2008). The coevolution of cultural groups and ingroup favoritism. Science, 321(5897), 1844–1849.

    Article  Google Scholar 

  16. 16.

    Eguíluz, V. M., Zimmermann, M. G., Cela-Conde, C. J., & Miguel, M. S. (2005). Cooperation and the emergence of role differentiation in the dynamics of social networks. American Journal of Sociology, 110(4), 977–1008.

    Article  Google Scholar 

  17. 17.

    Fehr, E., & Fischbacher, U. (2003). The nature of human altruism. Nature, 425(6960), 785–91.

    Article  Google Scholar 

  18. 18.

    Flache, A., & Macy, M. W. (2011). Local convergence and global diversity: From interpersonal to social influence. Journal of Conflict Resolution, 55(6), 970–995.

    Article  Google Scholar 

  19. 19.

    Flache, A., & Macy, M. W. (2011). Small worlds and cultural polarization. The Journal of Mathematical Sociology, 35(1–3), 146–176.

    Article  Google Scholar 

  20. 20.

    Flache, A., Mäs, M., Feliciani, T., Chattoe-Brown, E., Deffuant, G., Huet, S., et al. (2017). Models of social influence: Towards the next frontiers. Journal of Artificial Societies and Social Simulation, 20(4), 3521.

    Article  Google Scholar 

  21. 21.

    Fu, F., Hauert, C., Nowak, M. A., & Wang, L. (2008). Reputation-based partner choice promotes cooperation in social networks. Physical Review E, 78(2), 026117.

    Article  Google Scholar 

  22. 22.

    Fu, F., Tarnita, C. E., Christakis, N. A., Wang, L., Rand, D. G., & Nowak, M. A. (2012). Evolution of in-group favoritism. Scientific Reports, 2, 460.

    Article  Google Scholar 

  23. 23.

    Fu, F., Wu, T., & Wang, L. (2009). Partner switching stabilizes cooperation in coevolutionary prisoner’s dilemma. Physical Review E, 79(3), 036101.

    Article  Google Scholar 

  24. 24.

    Gallo, E., & Yan, C. (2015). The effects of reputational and social knowledge on cooperation. Proceedings of the National Academy of Sciences, 112(12), 201415883.

    Article  Google Scholar 

  25. 25.

    Gao, J., Li, Z., Wu, T., & Wang, L. (2011). The coevolutionary ultimatum game. EPL (Europhysics Letters), 93(4), 48003.

    Article  Google Scholar 

  26. 26.

    García, J., Veelen, M. V., & Traulsen, A. (2014). Evil green beards : Tag recognition can also be used to withhold cooperation in structured populations. Journal of Theoretical Biology, 360, 181–186.

    Article  Google Scholar 

  27. 27.

    Granovetter, M. S. (1973). The strength of weak ties. American Journal of Sociology, 78(6), 1360–1380.

    Article  Google Scholar 

  28. 28.

    Habyarimana, J., Humphreys, M., Posner, D. N., & Weinstein, J. M. (2007). Why does ethnic diversity undermine public goods provision? American Political Science Review, 101(04), 709–725.

    Article  Google Scholar 

  29. 29.

    Hardin, G. (1968). The tragedy of the commons. Science, 162(3859), 1243–1248.

    Article  Google Scholar 

  30. 30.

    Helbing, D., Szolnoki, A., Perc, M., & Szabó, G. (2010). Defector-accelerated cooperativeness and punishment in public goods games with mutations. Physical Review E, 81(5), 057104.

    Article  Google Scholar 

  31. 31.

    Howard, J. W., & Rothbart, M. (1980). Social categorization and memory for in-group and out-group behavior. Journal of Personality and Social Psychology, 38(2), 301–310.

    Article  Google Scholar 

  32. 32.

    Jackson, M. O. (2008). Social and economic networks. Princeton: Princeton University Press.

    Book  Google Scholar 

  33. 33.

    Kim, J. W. (2010). A tag-based evolutionary prisoner’s dilemma game on networks with different topologies. Journal of Artificial Societies and Social Simulation, 13(3), 1–20.

    Article  Google Scholar 

  34. 34.

    Kim, J. W., & Hanneman, R. A. (2014). Coevolutionary dynamics of cultural markers, parochial cooperation, and networks. Journal of Conflict Resolution, 58(2), 226–253.

    Article  Google Scholar 

  35. 35.

    Kollock, P. (1998). Social dilemmas: The anatomy of cooperation. Annual Review of Sociology, 24(1), 183–214.

    Article  Google Scholar 

  36. 36.

    Laakso, M., & Taagepera, R. (1979). “Effective” number of parties: A measure with application to West Europe. Computer Political Studies, 12(1), 3–27.

    Article  Google Scholar 

  37. 37.

    Larson, J. M., & Lewis, J. I. (2017). Ethnic networks. American Journal of Political Science, 61(2), 350–364.

    Article  Google Scholar 

  38. 38.

    Li, L. M. W., Adams, G., Kurtiş, T., & Hamamura, T. (2015). Beware of friends: The cultural psychology of relational mobility and cautious intimacy. Asian Journal of Social Psychology, 18(2), 124–133.

    Article  Google Scholar 

  39. 39.

    Macy, M., & Tsvetkova, M. (2015). The signal importance of noise. Sociological Methods and Research, 44(2), 306–328.

    Article  Google Scholar 

  40. 40.

    Macy, M. W., & Flache, A. (2002). Learning dynamics in social dilemmas. Proceedings of the National Academy of Sciences, 99(Supplement 3), 7229–7236.

    Article  Google Scholar 

  41. 41.

    Masuda, N. (2012). Ingroup favoritism and intergroup cooperation under indirect reciprocity based on group reputation. Journal of Theoretical Biology, 311, 8–18.

    Article  Google Scholar 

  42. 42.

    Masuda, N., & Fu, F. (2015). Evolutionary models of in-group favoritism. F1000Prime Reports, 7(March), 1–12.

    Google Scholar 

  43. 43.

    Masuda, N., & Ohtsuki, H. (2007). Tag-based indirect reciprocity by incomplete social information. Proceedings of the Royal Society B: Biological Sciences, 274(1610), 689–695.

    Article  Google Scholar 

  44. 44.

    McConnell, C., Margalit, Y., Malhotra, N., & Levendusky, M. (2018). The economic consequences of partisanship in a polarized era. American Journal of Political Science, 62(1), 5–18.

    Article  Google Scholar 

  45. 45.

    Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314(5805), 1560–1563.

    Article  Google Scholar 

  46. 46.

    Nowak, M. A., & May, R. M. (1992). Evolutionary games and spatial chaos. Nature, 359(6398), 826–829.

    Article  Google Scholar 

  47. 47.

    Nowak, M. A., & Sigmund, K. (1998). The dynamics of indirect reciprocity. Journal of Theoretical Biology, 194(4), 561–574.

    Article  Google Scholar 

  48. 48.

    Ohtsuki, H., Hauert, C., Lieberman, E., & Nowak, M. A. (2006). A simple rule for the evolution of cooperation on graphs and social networks. Nature, 441(7092), 502–505.

    Article  Google Scholar 

  49. 49.

    Olson, M. (1965). The logic of collective action : public goods and the theory of groups. Cambridge, Mass: Harvard University Press.

    Google Scholar 

  50. 50.

    Ostrom, E., Walker, J., & Gardner, R. (1992). Covenants with and without a sword: Self-governance is possible. American Political Science Review, 86(2), 404–417.

    Article  Google Scholar 

  51. 51.

    Pacheco, J. M., Traulsen, A., & Nowak, M. A. (2006). Coevolution of strategy and structure in complex networks with dynamical linking. Physical Review Letters, 97(25), 258103.

    Article  Google Scholar 

  52. 52.

    Perc, M., Jordan, J. J., Rand, D. G., Wang, Z., Boccaletti, S., & Szolnoki, A. (2017). Statistical physics of human cooperation. Physics Reports, 687, 1–51.

    Article  Google Scholar 

  53. 53.

    Perc, M., & Szolnoki, A. (2010). Coevolutionary games—A mini review. Biosystems, 99(2), 109–125.

    Article  Google Scholar 

  54. 54.

    Pinheiro, F. L., Santos, F. C., & Pacheco, J. M. (2016). Linking individual and collective behavior in adaptive social networks. Physical Review Letters, 116(12), 128702.

    Article  Google Scholar 

  55. 55.

    Przepiorka, W., Norbutas, L., & Corten, R. (2017). Order without law: Reputation promotes cooperation in a cryptomarket for illegal drugs. European Sociological Review, 33(6), 752–764.

    Article  Google Scholar 

  56. 56.

    Rand, D. G., Arbesman, S., & Christakis, N. A. (2011). Dynamic social networks promote cooperation in experiments with humans. Proceedings of the National Academy of Sciences, 108(48), 19193–19198.

    Article  Google Scholar 

  57. 57.

    Riolo, R. L., Cohen, M. D., & Axelrod, R. (2001). Evolution of cooperation without reciprocity. Nature, 414(6862), 441–443.

    Article  Google Scholar 

  58. 58.

    Sánchez, A. (2018). Physics of human cooperation: experimental evidence and theoretical models. Journal of Statistical Mechanics: Theory and Experiment, 2, 024001.

    Article  Google Scholar 

  59. 59.

    Santos, F. C., & Pacheco, J. M. (2005). Scale-free networks provide a unifying framework for the emergence of cooperation. Physical Review Letters, 95(9), 098104.

    Article  Google Scholar 

  60. 60.

    Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006). Cooperation prevails when individuals adjust their social ties. PLoS Computational Biology, 2(10), e140.

    Article  Google Scholar 

  61. 61.

    Santos, F. C., Rodrigues, J., & Pacheco, J. M. (2005). Epidemic spreading and cooperation dynamics on homogeneous small-world networks. Physical Review E, 72(5), 056128.

    Article  Google Scholar 

  62. 62.

    Santos, F. C., Rodrigues, J. F., & Pacheco, J. M. (2006). Graph topology plays a determinant role in the evolution of cooperation. Proceedings of the Royal Society B: Biological Sciences, 273(1582), 51–55.

    Article  Google Scholar 

  63. 63.

    Schug, J., Yuki, M., & Maddux, W. (2010). Relational mobility explains between- and within-culture differences in self-disclosure to close friends. Psychological Science, 21(10), 1471–1478.

    Article  Google Scholar 

  64. 64.

    Shirado, H., Fu, F., Fowler, J. H., & Christakis, N. A. (2013). Quality versus quantity of social ties in experimental cooperative networks. Nature Communications, 4(1), 2814.

    Article  Google Scholar 

  65. 65.

    Siegel, D. A. (2009). Social networks and collective action. American Journal of Political Science, 53(1), 122–138.

    Article  Google Scholar 

  66. 66.

    Simpson, B., & Willer, R. (2015). Beyond altruism: Sociological foundations of cooperation and prosocial behavior. Annual Review of Sociology, 41(1), 43–63.

    Article  Google Scholar 

  67. 67.

    Steinert-Threlkeld, Z. C. (2017). Spontaneous collective action: Peripheral mobilization during the arab spring. American Political Science Review, 111(2), 379–403.

    Article  Google Scholar 

  68. 68.

    Szolnoki, A., & Perc, M. (2009). Promoting cooperation in social dilemmas via simple coevolutionary rules. The European Physical Journal B, 67(3), 337–344.

    Article  Google Scholar 

  69. 69.

    Szolnoki, A., & Perc, M. (2017). Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment. Physical Review X, 7(4), 041027.

    Article  Google Scholar 

  70. 70.

    Tajfel, H. (1970). Experiments in intergroup discrimination. Scientific American, 223(5), 96–102.

    Article  Google Scholar 

  71. 71.

    Takesue, H. (2018). Evolutionary prisoner’s dilemma games on the network with punishment and opportunistic partner switching. EPL (Europhysics Letters), 121(4), 48005.

    Article  Google Scholar 

  72. 72.

    Takesue, H. (2019). Effects of updating rules on the coevolving prisoner’s dilemma. Physica A: Statistical Mechanics and its Applications, 513, 399–408.

    Article  Google Scholar 

  73. 73.

    Takesue, H., Ozawa, A., & Morikawa, S. (2017). Evolution of favoritism and group fairness in a co-evolving three-person ultimatum game. EPL (Europhysics Letters), 118(4), 48002.

    Article  Google Scholar 

  74. 74.

    Thomson, R., Yuki, M., & Ito, N. (2015). Computers in Human Behavior A socio-ecological approach to national differences in online privacy concern : The role of relational mobility and trust. Computers in Human Behavior, 51, 285–292.

    Article  Google Scholar 

  75. 75.

    Thomson, R., Yuki, M., Talhelm, T., Schug, J., Kito, M., Ayanian, A.H., Becker, J.C., Becker, M., Chiu, C.y., Choi, H.S., Ferreira, C.M., Fülöp, M., Gul, P., Houghton-Illera, A.M., Joasoo, M., Jong, J., Kavanagh, C.M., Khutkyy, D., Manzi, C., Marcinkowska, U.M., Milfont, T.L., Neto, F., von Oertzen, T., Pliskin, R., San Martin, A., Singh, P., & Visserman, M.L. (2018). Relational mobility predicts social behaviors in 39 countries and is tied to historical farming and threat. Proceedings of the National Academy of Sciences115(29), 7521–7526.

  76. 76.

    Traulsen, A., & Claussen, J. C. (2004). Similarity-based cooperation and spatial segregation. Physical Review E, 70(4), 046128.

    Article  Google Scholar 

  77. 77.

    Watts, D. J. (2004). The “new” science of networks. Annual Review of Sociology, 30(1), 243–270.

    Article  Google Scholar 

  78. 78.

    Yakubovich, V. (2005). Weak ties, information, and influence: How workers find jobs in a local russian labor market. American Sociological Review, 70(3), 408–421.

    Article  Google Scholar 

  79. 79.

    Yamagishi, T. (2011). Trust: The evolutionary game of mind and society. Tokyo: Springer.

    Book  Google Scholar 

  80. 80.

    Yang, Z., Li, Z., Wu, T., & Wang, L. (2013). Effects of adaptive dynamical linking in networked games. Physical Review E, 88(4), 042128.

    Article  Google Scholar 

  81. 81.

    Yuki, M., & Schug, J. (2012). Relational mobility: A socioecological approach to personal relationships. In O. Gillath, G. Adams, & A. Kunkel (Eds.), Relationship science: Integrating evolutionary, neuroscience, and sociocultural approaches (pp. 137–151). Washington, D.C.: American Psychological Association.

    Chapter  Google Scholar 

  82. 82.

    Zhang, C. Y., Zhang, J. L., Xie, G. M., & Wang, L. (2011). Coevolving agent strategies and network topology for the public goods games. European Physical Journal B, 80(2), 217–222.

    Article  Google Scholar 

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Correspondence to Hirofumi Takesue.

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Takesue, H. From defection to ingroup favoritism to cooperation: simulation analysis of the social dilemma in dynamic networks. J Comput Soc Sc 3, 189–207 (2020). https://doi.org/10.1007/s42001-019-00058-4

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Keywords

  • Ingroup favoritism
  • Prisoner’s dilemma
  • Agent-based modeling