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Cooperation in an evolutionary prisoner’s dilemma on networks with degree-degree correlations

Stephen Devlin1 and Thomas Treloar2

  • 1Mathematics Department, University of San Francisco, 2130 Fulton Street, San Francisco, California 94117, USA
  • 2Mathematics Department, Hillsdale College, 33 East College Street, Hillsdale, Michigan 49242, USA

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Phys. Rev. E 80, 026105 – Published 7 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026105

Abstract

We study the effects of degree-degree correlations on the success of cooperation in an evolutionary prisoner’s dilemma played on a random network. When degree-degree correlations are not present, the standardized variance of the network’s degree distribution has been shown to be an accurate analytical measure of network heterogeneity that can be used to predict the success of cooperation. In this paper, we use a local-mechanism interpretation of standardized variance to give a generalization to graphs with degree-degree correlations. Two distinct mechanisms are shown to influence cooperation levels on these types of networks. The first is an intrinsic measurement of base-line heterogeneity coming from the network’s degree distribution. The second is the increase in heterogeneity coming from the degree-degree correlations present in the network. A strong linear relationship is found between these two parameters and the average cooperation level in an evolutionary prisoner’s dilemma on a network.

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Corrections

11 August, 2009

Erratum

Publisher's Note: Cooperation in an evolutionary prisoner’s dilemma on networks with degree-degree correlations [Phys. Rev. E 80, 026105 (2009)]

Stephen Devlin and Thomas Treloar
Phys. Rev. E 80, 029902 (2009)

Comments & Replies

Comment on “Cooperation in an evolutionary prisoner’s dilemma on networks with degree-degree correlations”

Yun Zhu, Yuting Li, and Junzhong Yang
Phys. Rev. E 82, 038101 (2010)

See Also

Reply to “Comment on ‘Cooperation in an evolutionary prisoner’s dilemma on networks with degree-degree correlations’ ”

Stephen Devlin and Thomas Treloar
Phys. Rev. E 82, 038102 (2010)

Article Text

References (46)

  1. R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984).
  2. J. Maynard Smith, Evolution and the Theory of Games (Cambridge University Press, Cambridge, England, 1982).
  3. R. Axelrod, J. Conflict Resolut. 24, 379 (1980).
  4. H. Gintis, Game Theory Evolving (Princeton University, Princeton, NJ, 2000).
  5. Genetic and Cultural Evolution of Cooperation, edited by P. Hammerstein (MIT, Cambridge, MA, 2003).
  6. P. E. Turner and L. Chao, Nature (London) 398, 441 (1999).
  7. M. A. Nowak and R. M. May, Nature (London) 359, 826 (1992).
  8. G. Szabó and G. Fáth, Phys. Rep. 446, 97 (2007).
  9. F. C. Santos and J. M. Pacheco, Phys. Rev. Lett. 95, 098104 (2005).
  10. F. C. Santos and J. M. Pacheco, J. Evol. Biol. 19, 726 (2006).
  11. F. C. Santos, J. M. Pacheco, and T. Lenaerts, Proc. Natl. Acad. Sci. U.S.A. 103, 3490 (2006).
  12. F. C. Santos, J. F. Rodrigues, and J. M. Pacheco, Proc. R. Soc. London, Ser. B 273, 51 (2006).
  13. J. Gómez-Gardeñes, M. Campillo, L. M. Floría, and Y. Moreno, Phys. Rev. Lett. 98, 108103 (2007).
  14. G. Abramson and M. Kuperman, Phys. Rev. E 63, 030901(R) (2001).
  15. N. Masuda, Proc. R. Soc. London, Ser. B 274, 1815 (2007).
  16. A. Szolnoki, M. Perc, and Z. Danku, Physica A 387, 2075 (2008).
  17. M. Perc and A. Szolnoki, Phys. Rev. E 77, 011904 (2008).
  18. F. Santos, M. Santos, and J. Pacheco, Nature (London) 454, 213 (2008).
  19. A. Szolnoki, M. Perc, and Z. Danku, EPL 84, 50007 (2008).
  20. A. Szolnoki and G. Szabó, EPL 77, 30004 (2007).
  21. S. Devlin and T. Treloar, Phys. Rev. E 79, 016107 (2009).
  22. J. Poncela, J. Gómez-Gardeñes, L. M. Floría, and Y. Moreno, New J. Phys. 9, 184 (2007).
  23. A. Pusch, S. Weber, and M. Porto, Phys. Rev. E 77, 036120 (2008).
  24. C. Hauert, J. Theor. Biol. 240, 627 (2006).
  25. C. Hauert and M. Doebeli, Nature (London) 428, 643 (2004).
  26. M. Barthélemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. 92, 178701 (2004).
  27. M. Barthélemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, J. Theor. Biol. 235, 275 (2005).
  28. M. E. J. Newman, SIAM Rev. 45, 167 (2003).
  29. S. N. Dorogotsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University, Oxford, 2003).
  30. R. Albert and A.-L. Barabási, Science 286, 509 (1999).
  31. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
  32. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 64, 026118 (2001).
  33. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B 26, 521 (2002).
  34. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995).
  35. H. Ohtsuki, C. Hauert, E. Lieberman, and M. A. Nowak, Nature (London) 441, 502 (2006).
  36. P. M. Altrock and A. Traulsen, New J. Phys. 11, 013012 (2009).
  37. J. Gómez-Gardeñes and Y. Moreno, Phys. Rev. E 73, 056124 (2006).
  38. P. Erdős and A. Rényi, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5, 17 (1960).
  39. P. Erdős and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
  40. P. Erdős and A. Rényi, Acta. Math. Acad.Sci. Hung. 12, 261 (1961).
  41. Z. Rong, X. Li, and X. Wang, Phys. Rev. E 76, 027101 (2007).
  42. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).
  43. We have checked that our results are robust on networks down to a size of 2×103. For very small networks, of course, the mean-field parameters considered above become less meaningful and the evolutionary dynamics becomes more chaotic.
  44. The authors in [21] used additional uncorrelated networks as well.
  45. F. C. Santos, J. F. Rodrigues, and J. M. Pacheco, Phys. Rev. E 72, 056128 (2005).
  46. M. Perc, New J. Phys. 11, 033027 (2009).

Outline

Information

Phys. Rev. E 80, 026105– Published 7 August, 2009
  • Received 10 February 2009
  • Publisher error corrected 11 August 2009

© 2009 American Physical Society

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