The Effect of Group Size and Frequency-of-Encounter on the Evolution of Cooperation

  • Steve Phelps
  • Gabriel Nevarez
  • Andrew Howes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5778)


We introduce a model of the evolution of cooperation in groups which incorporates both conditional direct-reciprocity (“tit-for-tat”), and indirect-reciprocity based on public reputation (“conspicuous altruism”). We use ALife methods to quantitatively assess the effect of changing the group size and the frequency with which other group members are encountered. We find that for moderately sized groups, although conspicuous altruism plays an important role in enabling cooperation, it fails to prevent an exponential increase in the level of the defectors as the group size is increased, suggesting that economic factors may limit group size for cooperative ecological tasks such as foraging.


Group Size Indirect Reciprocity ALife Method Public Reputation Ecological Task 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ficici, S.G., Pollack, J.B.: Challenges in coevolutionary learning: Arms-race dynamics, open-endedness, and mediocre stable states. In: Proceedings of of ALIFE-6 (1998)Google Scholar
  2. 2.
    Ficici, S.G., Pollack, J.B.: A game-theoretic approach to the simple coevolutionary algorithm. In: Schwefel, H.-P., Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J. (eds.) PPSN VI 2000. LNCS, vol. 1917, pp. 16–20. Springer, Heidelberg (2000)Google Scholar
  3. 3.
    Hillis, W.D.: Co-evolving parasites improve simulated evolution as an optimization procedure. In: Langton, et al. (eds.) Proceedings of ALIFE-2, pp. 313–324. Addison Wesley, Reading (1992)Google Scholar
  4. 4.
    Miller, J.H.: The coevolution of automata in the repeated Prisoner’s Dilemma. Journal of Economic Behavior and Organization 29(1), 87–112 (1996)CrossRefGoogle Scholar
  5. 5.
    Nowak, M.A., Sigmund, K.: The alternating prisoner’s dilemma. Journal of Theoretical Biology 168, 219–226 (1994)CrossRefGoogle Scholar
  6. 6.
    Nowak, M.A., Sigmund, K.: The dynamics of indirect reciprocity. Journal of Theoretical Biology 194(4), 561–574 (1998)CrossRefGoogle Scholar
  7. 7.
    Nowak, M.A., Sigmund, K.: Evolution of indirect reciprocity by image scoring. Nature 383, 537–577 (1998)Google Scholar
  8. 8.
    Shampine, L.F., Reichelt, M.W.: The MATLAB ODE suite (2009),
  9. 9.
    Stafford, R.: Random vectors with fixed sum (January 2006),
  10. 10.
    Walsh, W.E., Das, R., Tesauro, G., Kephart, J.O.: Analyzing complex strategic interactions in multi-agent games. In: AAAI 2002 Workshop on Game Theoretic and Decision Theoretic Agents (2002),
  11. 11.
    Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1997) (First MIT Press edition)zbMATHGoogle Scholar
  12. 12.
    Wellman, M.P.: Methods for Empirical Game-Theoretic Analysis. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence, pp. 1152–1155 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Steve Phelps
    • 1
  • Gabriel Nevarez
    • 2
  • Andrew Howes
    • 2
  1. 1.Centre for Computational Finance and Economic Agents (CCFEA)University of EssexUK
  2. 2.Manchester Business SchoolUniversity of ManchesterUK

Personalised recommendations