Evolution of Mobile Strategies in Social Dilemma Games: An Analysis of Cooperative Cluster Formation

  • Maud D. GibbonsEmail author
  • Colm O’Riordan
  • Josephine Griffith
Part of the Studies in Computational Intelligence book series (SCI, volume 792)


This paper analyses the formation of cooperative clusters toward the emergence of cooperative clusters in evolutionary spatial game theory. In the model considered, agents inhabit a toroidal lattice grid, in which they participate in a social dilemma games, and have the ability to move in response to environmental stimuli. In particular, using the classical 2-player prisoner’s dilemma and a generalised N-player prisoner’s dilemma, we compare and contrast the evolved movement strategies, and the cooperative clusters formed therein. Additionally, we explore the effect of varying agent density on the evolution of cooperation, cluster formation, and the movement strategies that are evolved for both cooperative and non-cooperative strategies.



This work is funded by the Hardiman Research Scholarship, NUI Galway.


  1. 1.
    Axelrod, R.M.: The Evolution of Cooperation. Basic Books (1984)Google Scholar
  2. 2.
    Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press, New York (1982)CrossRefGoogle Scholar
  3. 3.
    Yao, X., Darwen, P.J.: An experimental study of N-person iterated prisoners dilemma games. Informatica 18, 435–450 (1994)zbMATHGoogle Scholar
  4. 4.
    Szolnoki, A., Perc, M., Szabó, G., Stark, H.U.: Impact of aging on the evolution of cooperation in the spatial prisoners dilemma game. Phys. Rev. E 80, 021901 (2009)CrossRefGoogle Scholar
  5. 5.
    Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)CrossRefGoogle Scholar
  6. 6.
    Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433, 312–316 (2005)CrossRefGoogle Scholar
  7. 7.
    Aktipis, C.A.: Know when to walk away: contingent movement and the evolution of cooperation. J. Theor. Biol. 231, 249–260 (2004)CrossRefGoogle Scholar
  8. 8.
    Vainstein, M.H., Silva, A.T.C., Arenzon, J.J.: Does mobility decrease cooperation? J. Theor. Biol. 244, 722–728 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gibbons, M.D., O’Riordan, C., Griffith, J.: Evolution of cooperation in n-player social dilemmas: the importance of being mobile. In: Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016), INSTICC, pp. 78–85. ScitePress (2016)Google Scholar
  10. 10.
    Boyd, R., Richerson, P.J.: The evolution of reciprocity in sizable groups. J. Theor. Biol. 132, 337–356 (1988)MathSciNetCrossRefGoogle Scholar
  11. 11.
    O’Riordan, C., Sorensen, H.: Stable cooperation in the N-player prisoners dilemma: the importance of community structure. In: Adaptive Agents and Multi-Agent Systems III. Adaptation and Multi-Agent Learning, pp. 157–168. Springer (2008)Google Scholar
  12. 12.
    Suzuki, R., Arita, T.: Evolutionary analysis on spatial locality in n-person iterated prisoner’s dilemma. Int. J. Comput. Int. Appl. 3, 177–188 (2003)CrossRefGoogle Scholar
  13. 13.
    Nowak, M.A.: Five rules for the evolution of cooperation. Science 314, 1560–3 (2006)CrossRefGoogle Scholar
  14. 14.
    Axelrod, R., Dion, D.: The further evolution of cooperation. Science 242, 1385–1390 (1988)CrossRefGoogle Scholar
  15. 15.
    Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)CrossRefGoogle Scholar
  16. 16.
    Santos, F., Rodrigues, J., Pacheco, J.: Graph topology plays a determinant role in the evolution of cooperation. Proc. R. Soc. B: Biol. Sci. 273, 51–55 (2006)CrossRefGoogle Scholar
  17. 17.
    Poncela, J., Gómez-Gardeñes, J., Floría, L.M., Moreno, Y., Sánchez, A.: Cooperative scale-free networks despite the presence of defector hubs. EPL (Europhys. Lett.) 88, 38003 (2009)CrossRefGoogle Scholar
  18. 18.
    Enquist, M., Leimar, O.: The evolution of cooperation in mobile organisms. Anim. Behav. 45, 747–757 (1993)CrossRefGoogle Scholar
  19. 19.
    Ichinose, G., Saito, M., Suzuki, S.: Collective chasing behavior between cooperators and defectors in the spatial prisoner’s dilemma. PLoS ONE 8, 28–31 (2013)CrossRefGoogle Scholar
  20. 20.
    Meloni, S., Buscarino, A., Fortuna, L., Frasca, M., Gómez-Gardeñes, J., Latora, V., Moreno, Y.: Effects of mobility in a population of prisoner’s dilemma players. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. 79, 3–6 (2009)CrossRefGoogle Scholar
  21. 21.
    Sicardi, E.A., Fort, H., Vainstein, M.H., Arenzon, J.J.: Random mobility and spatial structure often enhance cooperation. J. Theor. Biol. 256, 240–246 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Antonioni, A., Tomassini, M., Buesser, P.: Random diffusion and cooperation in continuous two-dimensional space. J. Theor. Biol. 344, 40–48 (2014)CrossRefGoogle Scholar
  23. 23.
    Helbing, D., Yu, W.: Migration as a mechanism to promote cooperation. Adv. Complex Syst. 11, 641–652 (2008)CrossRefGoogle Scholar
  24. 24.
    Helbing, D., Yu, W.: The outbreak of cooperation among success-driven individuals under noisy conditions. Proc. Natl. Acad. Sci. USA 106, 3680–3685 (2009)CrossRefGoogle Scholar
  25. 25.
    Jiang, L.L., Wang, W.X., Lai, Y.C., Wang, B.H.: Role of adaptive migration in promoting cooperation in spatial games. Phys. Rev. E 81, 036108 (2010)CrossRefGoogle Scholar
  26. 26.
    Yang, H.X., Wu, Z.X., Wang, B.H.: Role of aspiration-induced migration in cooperation. Phys. Rev. E 81, 065101 (2010)CrossRefGoogle Scholar
  27. 27.
    Tomassini, M., Antonioni, A.: Lévy flights and cooperation among mobile individuals. J. Theor. Biol. 364, 154–161 (2015)CrossRefGoogle Scholar
  28. 28.
    Joyce, D., Kennison, J., Densmore, O., Guerin, S., Barr, S., Charles, E., Thompson, N.S.: My way or the highway: a more naturalistic model of altruism tested in an iterative prisoners’ dilemma. J. Artif. Soc. Soc. Simul. 9, 4 (2006)Google Scholar
  29. 29.
    Gibbons, M., O’Riordan, C.: Evolution of coordinated behaviour in artificial life simulations. In: Proceedings of the International Conference on Theory and Practice in Modern Computing. (2014)Google Scholar
  30. 30.
    Gibbons, M.D., O’Riordan, C., Griffith, J.: Follow flee: A contingent mobility strategy for the spatial prisoners dilemma. In: International Conference on Simulation of Adaptive Behavior, pp. 34–45. Springer (2016)Google Scholar
  31. 31.
    Chiong, R., Kirley, M.: Random mobility and the evolution of cooperation in spatial N-player iterated prisoners dilemma games. Phys. A: Stat. Mech. Appl. 391, 3915–3923 (2012)CrossRefGoogle Scholar
  32. 32.
    Suarez, D., Suthaharan, P., Rowell, J., Rychtar, J.: Evolution of cooperation in mobile populations. Spora-A J. Biomath. 1, 2–7 (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maud D. Gibbons
    • 1
    Email author
  • Colm O’Riordan
    • 1
  • Josephine Griffith
    • 1
  1. 1.National University of IrelandGalwayIreland

Personalised recommendations