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Evolving Cooperation in the Spatial N-player Snowdrift Game

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AI 2010: Advances in Artificial Intelligence (AI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6464))

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Abstract

The Snowdrift game is a well-known social dilemma model frequently used in evolutionary game theory to investigate the emergence of cooperative behaviour under different biologically or socially plausible conditions. In this paper, we examine a multi-player version of the Snowdrift game where (i) the agents playing the game are mapped to the nodes of a regular two-dimensional lattice, (ii) the number of rounds of the game varies from a “one-shot” version to a fixed number of repeated interactions, and (iii) a genetic algorithm is used to evolve agent actions (strategy update) over a fixed number of generations. Comprehensive Monte Carlo simulation experiments show that cooperative behaviour is promoted in the multi-player iterated Snowdrift game. This emergent behaviour may be attributed to the combination of spatial reciprocity, based on the inherent capabilities of the genetic algorithm to explore the diverse sets of agents’ strategies, and repeated interactions. The simulation results also uncover some interesting findings regarding the effect of repeated interactions in the game.

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References

  1. Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)

    MATH  Google Scholar 

  2. 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 

  3. Chan, C.H., Yin, H., Hui, P.M., Zheng, D.F.: Evolution of Cooperation in well-mixed N-person Snowdrift Games. Physica A: Statistical Mechanics and its Applications 387, 2919–2925 (2008)

    Article  Google Scholar 

  4. Chen, X.-J., Wang, L.: Effects of Cost Threshold and Noise in Spatial Snowdrift Games with Fixed Multi-person Interactions. Europhysics Letters 90, 38003 (2010)

    Article  Google Scholar 

  5. Doebeli, M., Hauert, C.: Models of Cooperation based on the Prisoner’s Dilemma and the Snowdrift Game. Ecology Letters 8, 748–766 (2005)

    Article  Google Scholar 

  6. Gokhale, C.S., Traulsen, A.: Evolutionary Games in the Multiverse. Proceedings of the National Academy of Sciences of USA 107, 5500–5504 (2010)

    Article  MathSciNet  Google Scholar 

  7. Hauert, C., Doebeli, M.: Spatial Structure often Inhibits the Evolution of Cooperation in the Snowdrift Game. Nature 428, 643–646 (2004)

    Article  Google Scholar 

  8. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. MIT Press, Cambridge (1992)

    Google Scholar 

  9. Ji, M., Xu, C., Zheng, D.F., Hui, P.M.: Enhanced Cooperation and Harmonious Population in an Evolutionary N-person Snowdrift Game. Physica A: Statistical Mechanics and its Applications 389, 1071–1076 (2010)

    Article  Google Scholar 

  10. Lee, K.H., Chan, C.H., Hui, P.M., Zheng, D.F.: Cooperation in N-person Evolutionary Snowdrift Game in Scale-free Barabási–Albert Networks. Physica A: Statistical Mechanics and its Applications 387, 5602–5608 (2008)

    Article  Google Scholar 

  11. Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)

    Book  MATH  Google Scholar 

  12. Nowak, M.A., May, R.M.: Evolutionary Games and Spatial Chaos. Nature 359, 826–829 (1992)

    Article  Google Scholar 

  13. Nowak, M.A., May, R.M.: The Spatial Dilemmas of Evolution. International Journal of Bifurcation and Chaos 3, 35–78 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Souza, M.O., Pacheco, J.M., Santos, F.C.: Evolution of Cooperation under N-person Snowdrift Games. Journal of Theoretical Biology 260, 581–588 (2009)

    Article  MathSciNet  Google Scholar 

  15. Sysi-Aho, M., Saramäki, J., Kertész, J., Kaski, K.: Spatial Snowdrift Game with Myopic Agents. The European Physical Journal B 44, 129–135 (2005)

    Article  Google Scholar 

  16. Számadó, S., Szalai, F., Scheuring, I.: The Effect of Dispersal and Neighbourhood in Games of Cooperation. Journal of Theoretical Biology 253, 221–227 (2008)

    Article  MathSciNet  Google Scholar 

  17. Wang, W.-X., Ren, J., Chen, G., Wang, B.-H.: Memory-based Snowdrift Game on Networks. Physical Review E 74, 056113 (2006)

    Article  Google Scholar 

  18. Yao, X., Darwen, P.: An Experimental Study of N-person Iterated Prisoner’s Dilemma Games. Informatica 18, 435–450 (1994)

    MATH  Google Scholar 

  19. Zheng, D.F., Yin, H.P., Chan, C.H., Hui, P.M.: Cooperative Behavior in a Model of Evolutionary Snowdrift Games with N-person Interactions. Europhysics Letters 80, 18002 (2007)

    Article  MathSciNet  Google Scholar 

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Chiong, R., Kirley, M. (2010). Evolving Cooperation in the Spatial N-player Snowdrift Game. In: Li, J. (eds) AI 2010: Advances in Artificial Intelligence. AI 2010. Lecture Notes in Computer Science(), vol 6464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17432-2_27

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  • DOI: https://doi.org/10.1007/978-3-642-17432-2_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17431-5

  • Online ISBN: 978-3-642-17432-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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