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Prejudice, privilege, and power: Conflicts and cooperation between recognizable groups

1 Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa
2 African Institute for Mathematical Sciences, Cape Town 7945, South Africa

Special Issues: Mathematical Methods in the Biosciences

The problem of cooperation remains one of the fundamental questions in the fields of biology, sociology, and economics. The emergence and maintenance of cooperation are naturally affected by group dynamics, since individuals are likely to behave differently based on shared group membership. We here formulate a model of socio-economic power between two prejudiced groups, and explore the conditions for their cooperative coexistence under two social scenarios in a well-mixed environment. Each scenario corresponds to an asymmetrical increase in the payoffs for mutual cooperation in either cross-group or within-group interactions. In the ‘inter-dependence’ scenario payoffs of cross-group cooperation are enhanced, while in the ‘group-cohesion’ scenario payoffs of within-group cooperation are enhanced. We find that stable cooperative coexistence is possible only in the inter-dependence scenario. The conditions for such coexistence are highly sensitive to prejudice, defined as the reduction in probability for cross-group cooperation, and less sensitive to privilege, defined as the enhancements to payoffs of cross-group cooperation.
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1. T. Clutton-Brock, Cooperation between non-kin in animal societies, Nature, 462 (2009), 51–57.

2. R. L. Trivers, The evolution of reciprocal altruism, Q. Rev. Biol., 46 (1971), 35–57.

3. C. Darwin, On the origin of species by means of natural selection, or preservation of favoured races in the struggle for life. John Murray, London, 1859.

4. C. Hauert, M. Holmes and M. Doebeli, Evolutionary games and population dynamics: maintenance of cooperation in public goods games, Proc. R. Soc. B, 273 (2006), 2565–2570.

5. W. D. Hamilton, The genetical ecolution of social behavior I and II, J. Theor. Biol., 7 (1964), 1–52.

6. R. Axelrod, The Evolution of Cooperation, Basic Books, Inc., New York, 1981.

7. R. Boyd and P. J. Richerson, The evolution of indirect reciprocity, Social Networks, 11 (1989), 213 – 236.

8. M. A. Nowak and K. Sigmund, Evolution of indirect reciprocity, Nature, 437 (2005), 1291–1298.

9. A. Gardner and S. A. West, Greenbeards, Evolution, 64 (2009), 25–38.

10. S. D. Carroll, Evolutionary games and population dynamics, Q. Rev. Biol., 74 (1999), 347–347.

11. R. Boyd and P. J. Richerson, Culture and the evolution of human cooperation, Philos. Trans. R. Soc. B, 364 (2009), 3281–3288.

12. L. Liu, S. Wang, X. Chen, et al., Evolutionary dynamics in the public goods games with switching between punishment and exclusion, Chaos, 28 (2018), 103105.

13. X. Chen, T. Sasaki and M. Perc, Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement, Sci. Rep., 5 (2011).

14. M. Perc, J. Gomez-Gardenes, A. Szolnoki, et al., Evolutionary dymanics of group interactions on structured populations: a review, J. R. Soc. Interface, 10 (2013), 20120997.

15. A. Szolnoki and M. Perc, Second-order free-riding on antisocial punishment restores the effectiveness of prosocial punishment, Phys. Rev. X, 7 (2017), 198192.

16. K. Mahmoodi, B. J. West and P. Grigolini, Self-organizing Complex Networks: individual versus global rules, Front. Physiol., 8 (2017), 478.

17. M. Perc, J. J. Jordan, D. G. Rand, et al., Statistical physics of human cooperation Phys. Rep., 687 (2017), 1–51.

18. Z. Wang, L. Wang, A. Szolnoki, et al., Evolutionary games on multilayer networks: a colloquium,Eur. Phys. J. B, 88 (2015), 124.

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

20. K. M. Page and M. A. Nowak, Unifying evolutionary dynamics, J. Theor. Biol., 219 (2002), 93–98.

21. M. van Baalend and D. A. Rand The unit of selection in viscous populations and the evolution of altruism, J. Theor. Biol., 193 (1998), 631–648.

22. F. Zhang and C. Hui, Eco-evolutionary feedback and the invasion of cooperation in prisoner's dilemma games, PLoS One, 6 (2011), e27523.

23. F. Zhang, Y. Tao, Z. Li, et al., The evolution of cooperation on fragmented landscapes: the spatial hamilton rule, Evol. Ecol. Res., 12 (2010), 23–33.

24. P. Richerson, A .V. Bell, and R. Baldini et al., Cultural group selection plays an essential role in explaining human cooperation: A sketch of the evidence, Behav. Brain Sci., 29 (2016), 30.

25. B. C. Eaton, M. Eswaran and R. J. Oxoby, 'Us' and 'Them': The origin of identity, and its economic implications, Can. J. Econ., 44 (2011), 719–748.

26. R. M. Kramer and M. B. Brewer, Effects of group identity on resource use in a simulated commons dilemma, J. Pers. Soc. Psychol., 46 (1984), 1044–1057.

27. M. B. Brewer and R. M. Kramer, Choice behavior in social dilemmas: Effects of social identity, group size, and decision framing, J. Pers. Soc. Psychol., 50 (1986), 543–549.

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

29. D. H. Cole and P. Z. Grossman, Institutions matter! why the herder problem is not a prisoner's dilemma, Theo. Dec., 69 (2008), 219–231.

30. R. H. McAdams, Beyond the prisoners' dilemma: Coordination, game theory, and law, South. Calif. Law Rev., 82 (2009), 209.

31. B. Skyrms, The Stag Hunt and the Evolution of Social Structure, Cambridge University Press, 2003.

32. J.-J. Rousseau, R. D. Masters and C. Kelly, Discourse on the origins of inequality; polemics; and, political economy. Hanover, NH, Published for Dartmouth College by University Press of New England, 1992.

33. T. Antal, H. Ohtsuki, J. Wakeley, et al., Evolution of cooperation by phenotypic similarity, Proc. Natl. Acad. Sci. USA, 106 (2009), 8597–8600.

34. F. Fu, C. E. Tarnita, N. A. Christakis, et al., Evolution of in-group favoritism, Sci. Rep., 2 (2012), 460.

35. F. Jansson, What games support the evolution of an ingroup bias?, J. Theor. Biol., 373 (2015), 100–110.

36. W. A. Darity Jr, P. L. Mason and J. B. Stewart, The economics of identity: The origin and persistence of racial identity norms, J. Econ. Behav. Organ., 60 (2006), 283–305.

37. F. M. Kai and A. Konrad, Evolutionarily stable in-group favoritism and out-group spite in intergroup conflict, J. Theor. Biol., 306 (2012), 61–67.

38. N. Masuda, Ingroup favoritism and intergroup cooperation under indirect reciprocity based on group reputation, J. Theor. Biol., 311 (2012), 8–18.

39. K. Pattni, M. Broom and J. Rychtář, Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population, J. Theor. Biol., 429 (2017), 105–115.

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

41. J. P. Bruner, Diversity and cooperation, Ph.D thesis, UC Irvine, 2014.

42. S. T. Powers, D. J. Taylor and J. J. Bryson, Punishment can promote defection in group-structured populations, J. Theor. Biol., 311 (2012), 107–116.

43. C. Hui, P. Landi, H. O. Minoarivelo, et al., Ecological and Evolutionary Modelling, Springer International Publishing, 2018.

44. N. Alexander, Affirmative action and the perpetuation of racial identities in post-apartheid South Africa, Edited version of a Lecture originally delivered at the East London Campus, University of Fort Hare, 2006.

45. K. Durrheim, M. Xoliswa and L. Brown, Race trouble: race, identity and inequality in post- apartheid South Africa, Lexington Books, 2011.

46. R. A. Wilson, The politics of truth and reconciliation in South Africa: Legitimizing the post- apartheid state, Cambridge University Press, 2001.

47. N. Alexander, Language policy and national unity in South Africa/Azania, Buchu Books, Cape Town, 1989.

48. N. W. Thiong'o, Decolonizing the mind: the politics of language in African literature, James Currey, London, 1986.

49. P. Landi and F. Dercole, The social diversification of fashion, J. Math. Soc., 40 (2016), 185–205.

50. M. Hartshorn, A. Kaznatcheev and T. Schultz, The evolutionary dominance of ethnocentric cooperation, J. Artif. Soc. S., 16 (2013), 7.

51. R. Dawkins, The Selfish Gene, Oxford University Press, Oxford, UK, 1976.

52. V. A. A. Jansen and M. van Baalen, Altruism through beard chromodynamics, Nature, 440 (2006), 663.

53. A. Traulsen and M. A. Nowak, Chromodynamics of cooperation in finite populations, PLoS One,2 (2007), e270.

54. C. Hui, H. O. Minoarivelo and P. Landi, Modelling coevolution in ecological networks with adaptive dynamics, Math. Method. Appl. Sci., 41 (2018), 8407–8422.

55. M. Perc and A. Szolnoki Coevolutionary games - a mini review, BioSystems, 99 (2010), 109–125.

56. V. Capraro and M. Perc, Grand challenges in social physics: in pursuit of moral behavior, Front. Phys., 6 (2018), 107.

57. K. Mahmoodi, P. Grigolini and B. J. West, On social sensitivity to either zealot or independent minorities, Chaos, Soliton. Fract., 110 (2018), 185–190.

58. P. Landi and C. Piccardi, Community analysis in directed networks: in-, out- and pseudocommunities, Phys. Rev. E, 89 (2014), 012814.

59. K. Mahmoodi and P. Grigolini Evolutionary game theory and criticality J. Phys. A- Math. Theor., 50 (2017), 015101.

60. M.A.NowakandR.M.May, Evolutionarygamesandspatialchaos, Nature, 359(1992), 826–829.v 61. J. J. Horton, D. G. Rand and R. J. Zeckhauser, The online laboratory: conducting experiments in a real labor market. Exp. Econ., 14 (2011), 399–425.

62. A. Ofra and D. G. Rand, Economic games on the internet: the effect of $1 stakes, PloS One, 7 (2012), e31461.

63. D. G. Rand, The promise of Mechanical Turk: how online labor markets can help theorists run behavioural experiments, J. Theor. Biol., 299 (2012), 172–179.

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