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A Multi-agent Based Migration Model for Evolving Cooperation in the Spatial N-Player Snowdrift Game

  • Raymond Chiong
  • Michael Kirley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8291)

Abstract

In recent years, there has been an increased interest in using agent-based simulation models to investigate the evolution of cooperative behaviour in spatial evolutionary games. However, the relationship between individual player mobility (or migration) and population dynamics is not clear. In this paper, we investigate the impacts of alternative migration mechanisms in the spatial N-player Snowdrift game. Here, agents occupy sites in a two-dimensional toroidal lattice. Specific game instances are created by nominating N sites from each of the local neighbourhoods. We use a genetic algorithm to evolve agent game-playing strategies. In addition, agents have an opportunity to migrate to different sites in the lattice at regular intervals. Key parameters in our model include the migration rate, the actual dispersal distance, the “take-over” scheme, the group size N, and the relative cost-to-benefit ratio of the game. Detailed simulation experiments show that the proposed model is able to promote cooperation in a population of mobile agents. However, the magnitude of the dispersal distance plays a significant role in determining population dynamics. Our findings help to further understand how migratory (mobility) patterns affect evolutionary processes.

Keywords

Mobile Agent Cooperative Behaviour Public Good Game Moore Neighbourhood Focal Agent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aktipis, C.A.: Is cooperation viable in mobile organisms? Simple walk away rule favors the evolution of cooperation in groups. Evolution and Human Behavior 32(4), 263–276 (2011)CrossRefGoogle Scholar
  2. 2.
    Alba, E., Dorronsoro, B.: Cellular Genetic Algorithms. Springer, Berlin (2008)MATHGoogle Scholar
  3. 3.
    Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. IEEE Transactions on Evolutionary Computation 6(5), 443–462 (2002)CrossRefGoogle Scholar
  4. 4.
    Axelrod, R.: The evolution of strategies in the iterated prisoner’s dilemma. In: Davis, L. (ed.) Genetic Algorithms and Simulated Annealing, pp. 32–41. Morgan Kaufmann, Los Altos (1987)Google Scholar
  5. 5.
    Batty, M.: Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals. The MIT Press, Cambridge (2005)Google Scholar
  6. 6.
    Cantú-Paz, E.: A survey of parallel genetic algorithms. Calculateurs Parallèles, Réseaux et Systòmes Répartis 10(2), 141–171 (1998)Google Scholar
  7. 7.
    Cantú-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer, Norwell (2000)MATHGoogle Scholar
  8. 8.
    Chen, Z., Gao, J.X., Cai, Y.Z., Xu, X.M.: Evolution of cooperation among mobile agents. Physica A: Statistical Mechanics and its Applications 390, 1615–1622 (2011)CrossRefMATHGoogle Scholar
  9. 9.
    Chen, Z., Gao, J.X., Cai, Y.Z., Xu, X.M.: Evolutionary prisoner’s dilemma game in flocks. Physica A: Statistical Mechanics and its Applications 390, 50–56 (2011)CrossRefGoogle Scholar
  10. 10.
    Chiong, R., Dhakal, S., Jankovic, L.: Effects of neighbourhood structure on evolution of cooperation in N-player iterated prisoner’s dilemma. In: Yin, H., Tino, P., Corchado, E., Byrne, W., Yao, X. (eds.) IDEAL 2007. LNCS, vol. 4881, pp. 950–959. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Chiong, R., Kirley, M.: Evolving cooperation in the spatial N-player snowdrift game. In: Li, J. (ed.) AI 2010. LNCS, vol. 6464, pp. 263–272. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Chiong, R., Kirley, M.: Iterated N-player games on small-world networks. In: Krasnogor, N., Lanzi, P.L. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2011), pp. 1123–1130. ACM Press, New York (2011)Google Scholar
  13. 13.
    Chiong, R., Kirley, M.: Effects of iterated interactions in multi-player spatial evolutionary games. IEEE Transactions on Evolutionary Computation 16(4), 537–555 (2012)CrossRefGoogle Scholar
  14. 14.
    Chiong, R., Kirley, M.: The evolution of cooperation via stigmergic interactions. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2012), pp. 1052–1059. IEEE Press, Piscataway (2012)Google Scholar
  15. 15.
    Chiong, R., Kirley, M.: Random mobility and the evolution of cooperation in spatial N-player iterated prisoner’s dilemma games. Physica A: Statistical Mechanics and its Applications 391, 3915–3923 (2012)CrossRefGoogle Scholar
  16. 16.
    Dugatkin, L.A., Wilson, D.S.: ROVER: A strategy for exploiting cooperators in a patchy environment. The American Naturalist 138(3), 687–701 (1991)CrossRefGoogle Scholar
  17. 17.
    Enquist, M., Leimar, O.: The evolution of cooperation in mobile organisms. Animal Behaviour 45(4), 747–757 (1993)CrossRefGoogle Scholar
  18. 18.
    Guan, J.-Y., Wu, Z.-X., Wang, Y.-H.: Evolutionary snowdrift game with disordered environments in mobile societies. Chinese Physics 16(12), 3566–3570 (2007)CrossRefGoogle Scholar
  19. 19.
    Helbing, D., Yu, W.: Migration as a mechanism to promote cooperation. Advances in Complex Systems 11(4), 641–652 (2008)CrossRefMATHGoogle Scholar
  20. 20.
    Helbing, D., Yu, W.: The outbreak of cooperation among success-driven individuals under noisy conditions. Proceedings of the National Academy of Sciences of the United States of America 106, 3680–3685 (2009)CrossRefGoogle Scholar
  21. 21.
    Hofmann, L.-M., Chakraborty, N., Sycara, K.: The evolution of cooperation in self-interested agent societies: A critical study. In: Sonenberg, L., Stone, P., Tumer, K., Yolum, P. (eds.) Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), Taipei, Taiwan, pp. 685–692 (2011)Google Scholar
  22. 22.
    Jiang, L.-L., Wang, W.-X., Lai, Y.-C., Wang, B.-H.: Role of adaptive migration in promoting cooperation in spatial games. Physical Review E 81(3), 36108 (2010)CrossRefGoogle Scholar
  23. 23.
    Killingback, T., Doebeli, M.: Spatial evolutionary game theory: Hawks and doves revisited. Proceedings of the Royal Society of London: Biological Sciences 263, 1135–1144 (1996)CrossRefGoogle Scholar
  24. 24.
    Kirchkamp, O.: Spatial evolution of automata in the prisoners’ dilemma. Journal of Economic Behaviour and Organization 43(2), 239–262 (2000)CrossRefGoogle Scholar
  25. 25.
    Kirley, M.: A cellular genetic algorithm with disturbances: Optimisation using dynamic spatial interactions. Journal of Heuristics 8(3), 321–342 (2002)CrossRefMATHGoogle Scholar
  26. 26.
    Kümmerli, R., Gardner, A., West, S.A., Griffin, A.S.: Limited dispersal, budding dispersal, and cooperation: An experimental study. Evolution 63(4), 939–949 (2009)CrossRefGoogle Scholar
  27. 27.
    Kun, A., Scheuring, I.: The evolution of density-dependent dispersal in a noisy spatial population model. Oikos 115, 308–320 (2006)CrossRefGoogle Scholar
  28. 28.
    Lambin, X., Aars, J., Piertney, S.B.: Dispersal, intraspecific competition, and kin facilitation: A review of the empirical evidence. In: Clobert, J., Danchin, E., Dhondt, A.A., Nichols, J.D. (eds.) Dispersal, pp. 110–122. Oxford University Press (2001)Google Scholar
  29. 29.
    Lin, Y.-T., Yang, H.-X., Wu, Z.-X., Wang, B.-H.: Promotion of cooperation by aspiration-induced migration. Physica A: Statistical Mechanics and its Applications 390, 77–82 (2011)CrossRefGoogle Scholar
  30. 30.
    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. Physical Review E 79(6), 067101 (2009)CrossRefGoogle Scholar
  31. 31.
    Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)CrossRefGoogle Scholar
  32. 32.
    Nowak, M.A., May, R.M.: The spatial dilemmas of evolution. International Journal of Bifurcation and Chaos 3, 35–78 (1993)MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Ono, M., Ishizuka, M.: Prisoner’s dilemma game on network. In: Lukose, D., Shi, Z. (eds.) PRIMA 2005. LNCS, vol. 4078, pp. 33–44. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  34. 34.
    O’Reilly, G.B., Ehlers, E.: Synthesizing stigmergy for multi agent systems. In: Shi, Z.-Z., Sadananda, R. (eds.) PRIMA 2006. LNCS (LNAI), vol. 4088, pp. 34–45. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  35. 35.
    Perrin, N., Goudet, J.: Inbreeding, kinship, and the evolution of natal dispersal. In: Clobert, J., Danchin, E., Dhondt, A.A., Nichols, J.D. (eds.) Dispersal, pp. 123–142. Oxford University Press (2001)Google Scholar
  36. 36.
    Santos, F.C., Pacheco, J.M.: Scale-free networks provide a unifying framework for the emergence of cooperation. Physical Review Letters 95, 098104 (2005)CrossRefGoogle Scholar
  37. 37.
    Schtickzelle, N., Fjerdingstad, E.J., Chaine, A., Clobert, J.: Cooperative social clusters are not destroyed by dispersal in a ciliate. BMC Evolutionary Biology 9, 251 (2009)CrossRefGoogle Scholar
  38. 38.
    Sicardi, E.A., Fort, H., Vainstein, M.H., Arenzon, J.J.: Random mobility and spatial structure often enhance cooperation. Journal of Theoretical Biology 256, 240–246 (2009)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Suzuki, S., Kimura, H.: Oscillatory dynamics in the coevolution of cooperation and mobility. Journal of Theoretical Biology 287, 42–47 (2011)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Sysi-Aho, M., Saramäki, J., Kertész, J., Kaski, K.: Spatial snowdrift game with myopic agents. The European Physical Journal B 44(1), 129–135 (2005)CrossRefGoogle Scholar
  41. 41.
    Szabó, G., Fáth, G.: Evolutionary games on graphs. Physics Reports 446, 97–216 (2007)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Vainstein, M.H., Silva, A.T.C., Arenzon, J.J.: Does mobility decrease cooperation? Journal of Theoretical Biology 244, 722–728 (2007)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Weidlich, W.: Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences. Harwood Academic Publishers, Amsterdam (2000)Google Scholar
  44. 44.
    Yang, H.X., Wang, W.X., Wang, B.H.: Universal role of migration in the evolution of cooperation. physics.soc-ph, page arXiv:1005.5453v1 (2010)Google Scholar
  45. 45.
    Yang, H.-X., Wu, Z.-X., Wang, B.-H.: Role of aspiration-induced migration in cooperation. Physical Review E 81(6), 065101 (2010)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Yao, X., Darwen, P.: An experimental study of N-person iterated prisoner’s dilemma games. Informatica 18(4), 435–450 (1994)MATHGoogle Scholar
  47. 47.
    Zhang, J., Wang, W.-Y., Du, W.-B., Cao, X.-B.: Evolution of cooperation among mobile agents with heterogenous view radii. Physica A: Statistical Mechanics and its Applications 390, 2251–2257 (2011)CrossRefGoogle Scholar
  48. 48.
    Zhang, J., Zhang, C., Chu, T.: The evolution of cooperation in spatial groups. Chaos, Solitons and Fractals 44, 131–136 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Raymond Chiong
    • 1
  • Michael Kirley
    • 2
  1. 1.School of Design, Communication and Information Technology, Faculty of Science and Information TechnologyThe University of NewcastleCallaghanAustralia
  2. 2.Department of Computing and Information Systems, Melbourne School of EngineeringThe University of MelbourneParkvilleAustralia

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