Effects of directional migration on prisoner’s dilemma game in a square domain

  • Hongyan Cheng
  • Qionglin Dai
  • Haihong Li
  • Xiaolan Qian
  • Mei Zhang
  • Junzhong Yang
Regular Article

Abstract

We introduce a new migration rule, the directional migration, into evolutionary prisoner’s dilemma games defined in a square domain with periodic boundary conditions. We find that cooperation can be enhanced to a much higher level than the case in the absence of migration. Additionally, the presence of the directional migration has profound impact on the population structure: the directional migration drives individuals to form a number of dense clusters which resembles social cohesion. The evolutionary game theory incorporating the directional migration can reproduce some real characteristics of populations in human society and may shed light on the problem of social cohesion.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    J. Weibull, Evolutionary Game Theory (MIT Press, Cambridge, 1995)Google Scholar
  2. 2.
    R. Axelrod, W.D. Hamilton, Science 211, 1390 (1981)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    W.D. Hamiltion, J. Theor. Biol. 7, 17 (1964)CrossRefGoogle Scholar
  4. 4.
    R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984)Google Scholar
  5. 5.
    M.A. Nowak, K. Sigmund, Nature 437, 1291 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    A. Traulsen, M.A. Nowak, Proc. Natl. Acad. Sci. 103, 10952 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    M.A. Nowak, R.M. May, Nature 359, 826 (1992)ADSCrossRefGoogle Scholar
  8. 8.
    G. Szabó, C. Toke, Phys. Rev. E 58, 69 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    J. Vukov, G. Szabó, A. Szolnoki, Phys. Rev. E 73, 067103 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    C. Hauert, G. Szabó, Am. J. Phys. 73, 405 (2005)ADSMATHCrossRefGoogle Scholar
  11. 11.
    F.C. Santos, J.F. Rodrigues, J.M. Pacheco, Phys. Rev. E 72, 056128 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    F.C. Santos, J.M. Pacheco, Phys. Rev. Lett. 95, 098104 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    F.C. Santos, J.M. Pacheco, T. Lenaerts, Proc. Natl. Acad. Sci. 103, 3490 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    J. Gómez-Gardenes, M. Campillo, L.M. Floría, Y. Moreno, Phys. Rev. Lett. 98, 108103 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    A. Pusch, S. Weber, M. Porto, Phys. Rev. E 77, 036120 (2008)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    M. Perc, New J. Phys. 11, 033027 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    M.A. Nowak, Science 314, 314 (2006)CrossRefGoogle Scholar
  18. 18.
    C. Hauert, S. De Monte, J. Hofbauer, K. Sigmund, Science 296, 1129 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    A. Szolnoki, N.G. Xie, C. Wang, M. Perc, Europhys. Lett. 96, 38002 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    M.G. Zimmermann, V.M. Eguíluz, M. San Miguel, Phys. Rev. E 69, 065102(R) (2004)ADSCrossRefGoogle Scholar
  21. 21.
    F.C. Santos, J.M. Pacheco, T. Lenaerts, PLOS Comput. Biol. 2, e140 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    J.M. Pacheco, A. Traulsen, M.A. Nowak, Phys. Rev. Lett. 97, 258103 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    S.V. Segbroeck, F.C. Santos, A. Nowé, J.M. Pacheco, T. Lenaerts, BMC Evol. Biol. 8, 287 (2008)CrossRefGoogle Scholar
  24. 24.
    M. Perc, A. Szolnoki, G. Szabó, Phys. Rev. E, 78, 066101 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    S. Van Segbroeck, F.C. Santos, T. Lenaerts, J.M. Pacheco, Phys. Rev. Lett. 102, 058105 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    F. Fu, T. Wu, L. Wang, Phys. Rev. E 79, 036101 (2009)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    W.X. Wang, J. Ren, G. Chen, B.H. Wang, Phys. Rev. E 74, 056113 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    A. Szolnoki, M. Perc, New J. Phys. 10, 043036 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    A. Szolnoki, G. Szabó, Europhys. Lett. 77, 30004 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    G. Szabó, A. Szolnoki, Phys. Rev. E 79, 016106 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    F.C. Santos, M.D. Santos, J.M. Pacheco, Nature 454, 213 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    M. Perc, A. Szolnoki, Phys. Rev. E 77, 011904 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    M.H. Vainstein, J.J. Arenzon, Phys. Rev. E 64, 051905 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    M.H. Vainstein, A.T.C. Silva, J.J. Arenzon, J. Theor. Biol. 244, 722 (2007)MathSciNetCrossRefGoogle Scholar
  35. 35.
    D. Helbing, W. Yu, Adv. Complex Syst. 11, 641 (2008)MATHCrossRefGoogle Scholar
  36. 36.
    D. Helbing, W. Yu, Proc. Natl. Acad. Sci. 106, 3680 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    S. Meloni, A. Buscarino, L. Fortuna, M. Frasca, J. Gómez-Gardenes, V. Latora, Y. Moreno, Phys. Rev. E 79, 067101 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    M. Droz, J. Szwabiński, G. Szabó, Eur. Phys. J. B 71, 579 (2009)ADSMATHCrossRefGoogle Scholar
  39. 39.
    H.X. Yang, Z.X. Wu, B.H. Wang, Phys. Rev. E 81, 065101(R) (2010)ADSGoogle Scholar
  40. 40.
    H.Y. Cheng, H.H. Li, Q.L. Dai, J.Z. Yang, New J. Phys. 12, 123014 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    H.Y. Cheng, Q.L. Dai, H.H. Li, Y. Zhu, M. Zhang, J.Z. Yang, New J. Phys. 13, 043032 (2011)ADSCrossRefGoogle Scholar
  42. 42.

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hongyan Cheng
    • 1
  • Qionglin Dai
    • 1
  • Haihong Li
    • 1
  • Xiaolan Qian
    • 2
  • Mei Zhang
    • 3
  • Junzhong Yang
    • 1
  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingP.R. China
  2. 2.School of Electronics and InformationZhejiang University of Media and CommunicationsHangzhouP.R. China
  3. 3.Department of PhysicsBeijing Normal UniversityBeijingP.R. China

Personalised recommendations