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Stable Cooperation in the N-Player Prisoner’s Dilemma: The Importance of Community Structure

  • Colm O’Riordan
  • Humphrey Sorensen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4865)

Abstract

N-player prisoner dilemma games have been adopted and studied as a representation of many social dilemmas. They capture a larger class of social dilemmas than the traditional two-player prisoner’s dilemma. In N-player games, defection is the individually rational strategy and normally emerges as the dominant strategy in evolutionary simulations of agents playing the game.

In this paper, we discuss the effect of a specific type of spatial constraint on a population of learning agents by placing agents on a graph structure which exhibits a community structure. We show that, by organising agents on a graph with a community structure, cooperation can exist despite the presence of defectors. Furthermore, we show that, by allowing agents learn from agents in neighbouring communities, cooperation can actually spread and become the dominant robust strategy.

Moreover, we show that the spread of cooperation is robust to the introduction of noise into the system.

Keywords

Cooperation N-Player Prisoner’s dilemma Community structure 

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References

  1. 1.
    Bendor, J.: Uncertainty and the Evolution of Cooperation. Journal of Conflict Resolution 37(4), 709–734 (1993)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Boyd, R., Richerson, P.J.: The Evolution of Reciprocity in Sizable Groups. Journal of Theoretical Biology 132, 337–356 (1988)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Davis, J.H., Laughlin, P.R., Komorita, S.S.: The social psychology of small groups: Cooperative and Mixed-Motive Interaction. Annual review of Psychology 27, 501–541 (1976)CrossRefGoogle Scholar
  4. 4.
    Doneeti, L., Munoz, M.A.: Detecting network communities: a new systematic and powerful algorithm. Journal of Statistical Mechanics, P10012  (October 2004)Google Scholar
  5. 5.
    Hardin, G.: The tragedy of the commons. Science 162(3859), 1243–1248 (1968)CrossRefGoogle Scholar
  6. 6.
    Hauert, C.: Spatial Effects in Social Dilemmas. Journal of Theoretical Biology 240(4), 627–636 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kraines, D., Kraines, V.: Learning to Cooperate with Pavlov: An adaptive strategy for the Iterated Prisoner’s Dilemma with Noise. Theory and Decision 35, 107–150 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Lindgren, K., Nordahl, M.G.: Evolutionary Dynamics of Spatial Games. Physica D 75(1-3), 292–309 (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    Lozano, S., Arenas, A., Sanchez, A.: Mesoscopic structure conditions the emergence of cooperation on social networks. arXiv:physics/0612124v1 (2006)Google Scholar
  10. 10.
    Moran, M., O’Riordan, C.: Emergence of Cooperative Societies in Structured Multi-agent systems.In: AICS 2005. Proceedings of the 16th Irish Conference on Artificial Intelligence and Cognitive Science  (September 2005)Google Scholar
  11. 11.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physics Review E 69 (2004)Google Scholar
  12. 12.
    Nowak, M.A., May, R.M., Bonhoffer, S.: More Spatial Games. International Journal of Bifurcation and Chaos 4(1), 33–56 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Nowak, M.A., Sigmund, K.: Games on Grids. In: Dieckmann, U., Law, R., Metz, J.A.J. (eds.) The Geometry of Ecological Interaction, pp. 135–150. Cambridge University Press, Cambridge (2000)Google Scholar
  14. 14.
    O’Riordan, C.: Evolving Strategies for Agents in the Iterated Prisoner’s Dilemma in Noisy Environments. AISB: Cognition in Machines and Animals  (April 2003)Google Scholar
  15. 15.
    Ramchurn, S., Huynh, D., Jennings, N.R.: Trust in multiagent systems. The Knowledge Engineering Review 19(1), 1–25 (2004)CrossRefGoogle Scholar
  16. 16.
    Riolo, R.L.: The Effects of Tag-Mediated Selection of Partners in Evolving Populations Playing the Iterated Prisoner’s Dilemma. Technical report, Santa Fe Institute Working Paper 97-02-016 (1997)Google Scholar
  17. 17.
    O’ Riordan, C., Griffith, J., Newell, J., Sorensen, H.: Co-evolution of strategies for an N-player dilemma. In: Proceedings of the Congress on Evolutionary Computation (June 19-23, 2004)Google Scholar
  18. 18.
    Santos, F.C, Pacheco, J.M., Lenaerts, T.: Cooperation Prevails when Individuals Adjust Their Social Ties. PLOS Compuational Biology 2(10) (October 2006)Google Scholar
  19. 19.
    Santos, F.C, Pacheo, J.M.: Scale-free Networks Provide a Unifying Framework for the Emergence of Cooperation. Physical Review Letters 95(9) (August 2005)Google Scholar
  20. 20.
    Smucker, M.D., Stanley, E.A., Ashlock, D.: Analyzing Social Network Structures in the Iterated Prisoner’s Dilemma with Choice and Refusal. Technical report, University of Wisconsin, Technical Report CS-TR-94-1259 (December 1994)Google Scholar
  21. 21.
    Wu, J., Axelrod, R.: How to Cope with Noise in the Iterated Prisoner’s Dilemma. Journal of Conflict Resolution 39(1), 183–189 (1995)CrossRefGoogle Scholar
  22. 22.
    Wu, Z., Xu, X., Chen, Y., Wang, Y.: Spatial prisoner’s dilemma game with volunteering in newman-watts small-world networks. Physical Review E 71, 37103 (2005)CrossRefGoogle Scholar
  23. 23.
    Wu, Z., Xu, X., Wang, Y.: Does the scale-free topology favor the emergence of cooperation? eprint arXiv physics/0508220  (2005)Google Scholar
  24. 24.
    Wu, Z., Xu, X., Wang, Y.: Prisoner’s dilemma game with heterogenuous influence effect on regular small world networks. Chinese Physics Letters  (2005)Google Scholar
  25. 25.
    Yao, X., Darwen, P.J.: An experimental study of N-person iterated prisoner’s dilemma games. Informatica 18, 435–450 (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Colm O’Riordan
    • 1
  • Humphrey Sorensen
    • 2
  1. 1.Dept. of Information TechnologyNUIGalwayIreland
  2. 2.Dept. of Computer ScienceUniversity College CorkIreland

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