Advertisement

Cooperation in Heterogeneous Populations

  • Karl Sigmund
  • Martin Nowak
Chapter
Part of the Recent Research in Psychology book series (PSYCHOLOGY)

Abstract

This paper deals with stochastic reactive strategies for the Iterated Prisoner’s Dilemma. It considers populations of individuals meeting randomly, and noisy interactions. Both the analysis of monomorphic and heteromorphic populations show that the reciprocal strategy Tit For Tat acts like a pivot: it triggers an evolution towards cooperation, but is not the ultimate beneficiary of such an evolution.

Keywords

Heterogeneous Population Game Dynamic Vervet Monkey Previous Round Reciprocal Altruism 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Axelrod R. (1984). The evolution of cooperation. New York: Basic Books Inc. (reprinted by Penguin, Harmondsworth)Google Scholar
  2. Axelrod, R. (1987). The evolution of strategies in the iterated prisoner’s dilemma. In D. Davis (Ed.), Genetic algorithms and simulated annealing (pp. 32–43). London: Pitman.Google Scholar
  3. Axelrod, R., & Dion, D. (1988). The further evolution of cooperation, Science, 242, 1385–1390.PubMedCrossRefGoogle Scholar
  4. Axelrod, R., & Hamilton, W.D. (1981). The evolution of cooperation. Science, 211, 1390–1396.PubMedCrossRefGoogle Scholar
  5. Cheney, D.L., & Seyfarth, D. (1982). Recognition of individuals within and between groups of free-ranging vervet monkeys. American Zoologist, 22, 519–529.Google Scholar
  6. Fischer, E.A. (1980). The relationship between mating system and simultaneous hermaphroditism in the coral reef fish. Hypoplectrus nigricans. Animal Behaviour, 28, 620–633.CrossRefGoogle Scholar
  7. Hofbauer, J., & Sigmund, K. (1988). The theory of evolution and dynamical systems. Cambridge: Cambridge University Press.Google Scholar
  8. Hofstadter, D. (1985). Metamagical themas: Questing for the essence of mind and pattern. New York: Basic Books.Google Scholar
  9. Lindgren, K. (1991) Evolutionary phenomena in simple dynamics. In Langton et al. (Eds.), Artificial Life II (pp. 295–312), Proceedings of the Santa Fe Institute Studies, Addison-Wesley.Google Scholar
  10. Luce, R.D., & Raiffa, H. (1957). Games and decisions. New York: Wiley.Google Scholar
  11. May, R.M. (1987). More evolution of cooperation. Nature, 327, 15–17.CrossRefGoogle Scholar
  12. Micko, H.-Ch., Brückner, G., & Ratzke, H. (1977). Theories and strategies for prisoner’s dilemma. In W.F. Kempf & B.H. Repp (Eds.), Mathematical Models for Social Psychology (pp. 214–276). Bern: Huber.Google Scholar
  13. Milinski, M. (1987). Tit for tat in sticklebacks and the evolution of cooperation. Nature, 325, 434–435.CrossRefGoogle Scholar
  14. Molander, P. (1985). The optimal level of generosity in a selfish, uncertain environment. Journal of Conflict Resolution, 29, 611–618.CrossRefGoogle Scholar
  15. Nowak, M. (1990). An evolutionarily stable strategy may be inaccessible, Theoretical Population in Biology, 142, 237–241.Google Scholar
  16. Nowak, M., & Sigmund, K. (1989a). Oscillations in the evolution of reciprocity. Journal of Theoretical Biology, 147, 21–26.CrossRefGoogle Scholar
  17. Nowak, M., & Sigmund, K. (1989b). Game dynamical aspects of the prisoner’s dilemma. Journal of Applied Mathematics and Computation, 30, 191–213.CrossRefGoogle Scholar
  18. Nowak, M. & Sigmund, K. (1990). The evolution of reactive strategies in iterated games. Acta Applicandae Mathematicae, 20, 247–265.CrossRefGoogle Scholar
  19. Nowak, M., & Sigmund, K. (1992). Tit for tat in heterogeneous populations. Nature, 353, 250–253.CrossRefGoogle Scholar
  20. Packer, C. (1979). Reciprocal altruism in Papio anubis. Nature, 265, 441–443.CrossRefGoogle Scholar
  21. Trivers, R. (1985). Social evolution. Menlo Park: Benjamin-Cummings.Google Scholar
  22. Selten, R., & Stoecker, R. (1986). End behaviour in sequences of finite prisoner’s dilemma supergames. Journal of Economical Behavior and Organization, 7, 47–70.CrossRefGoogle Scholar
  23. Wilkinson, G.S. (1984). Reciprocal food sharing in the vampire bat. Nature, 308, 181–184.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Karl Sigmund
    • 1
  • Martin Nowak
    • 2
  1. 1.Department of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of ZoologyUniversity of OxfordOxfordEngland

Personalised recommendations