Theory and Decision

, Volume 55, Issue 4, pp 289–314 | Cite as

The Emergence of Reactive Strategies in Simulated Heterogeneous Populations

  • Ilan Fischer


The computer simulation study explores the impact of the duration of social impact on the generation and stabilization of cooperative strategies. Rather than seeding the simulations with a finite set of strategies, a continuous distribution of strategies is being defined. Members of heterogeneous populations were characterized by a pair of probabilistic reactive strategies: the probability to respond to cooperation by cooperation and the probability to respond to defection by cooperation. This generalized reactive strategy yields the standard TFT mechanism, the All-Cooperate, All-Defect and Bully strategies as special cases. Pairs of strategies interacted through a Prisoner's Dilemma game and exerted social influence on all other members. Manipulating: (i) the initial distribution of populations' strategies, and (ii) the duration of social influence, we monitored the conditions leading to the emergence and stabilization of cooperative strategies. Results show that: (1) The duration of interactions between pairs of strategies constitutes a crucial factor for the emergence and stabilization of cooperative strategies, (2) Unless sufficient learning intervals are provided, initializing the simulations with cooperative populations does not guarantee that cooperation will sustain.

computer simulation duration of interaction heterogeneous populations Prisoner's Dilemma probabilistic Tit For Tat reactive strategies social impact 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Auman, R.J. and Maschler, M.B. (1995), Repeated Games with Incomplete Information, The MIT Press, Cambridge, Massachusetts, p.236.Google Scholar
  2. Axelrod, R. (1980a), Effective choice in the Prisoner's Dilemma, Journal of Conflict Resolution 24, 3–25.Google Scholar
  3. Axelrod, R. (1980b), More effective choice in the Prisoner's Dilemma, Journal of Conflict Resolution, 24, 379–403.Google Scholar
  4. Axelrod, R. (1981), The emergence of cooperation among egoists, The American Political Science Review, 75, 306–318.Google Scholar
  5. Axelrod, R. (1984), The Evolution of Cooperation, Basic Books, New York.Google Scholar
  6. Axelrod, R. (1997), Evolving new strategies: The evolution of strategies in the iterated Prisoner's Dilemma, in R. Axelrod (ed.), The Complexity of Cooperation Princeton University Press: New Jersey, pp. 41–29.Google Scholar
  7. Bendor, J. (1987), In good times and bad: Reciprocity in an uncertain world, American Journal of Political Science 31, 531–538.Google Scholar
  8. Bendor, J., Kramer, R.M., and Stout, S. (1991), When in doubt: Cooperation in a noisy Prisoner's Dilemma, Journal of Conflict Resolution 35, 691–719.Google Scholar
  9. Chattoe, E. (1998), Just How (Un)realistic are Evolutionary Algorithms as Representations of Social Process? Journal of Artificial Societies and Social 1, 3, Simulation, available online>.Google Scholar
  10. Derman, C., Gleser, L.J. and Olkin, I. (1973), A Guide to Probability Theory and Application, Holt, Rinehart, and Winston: New York.Google Scholar
  11. Dugatkin, L.A. and Alfieri, M. (1991), Tit-for-tat in guppies (Poecilla reticulata): the relative nature of cooperation and defection during predator inspection, Evolutionary Ecology 5, 300–309.Google Scholar
  12. Fischer, I. (2003), Evolutionary development and learning: two facets of strategy generation, Journal of Artificial Societies and Social Simulations 6(1), available online Scholar
  13. Fischer, I. and Suleiman, R., (1997), Mutual cooperation in a simulated intergroup conflict, Journal of Conflict Resolution, 41(4), 483–508.Google Scholar
  14. Fogel, D.B. (1993), Evolutionary Computation: Towards a New Philosophy of Machine Intelligence, IEEE Press, New York.Google Scholar
  15. Gorrini, V. and Dorigo, M. (1996), An application of evolutionary algorithms to the scheduling of robotic operations, in Alliot, J.M., Lutton, E., Ronald, E., and Schoenauer, M. (eds.), Artificial Evolution. AnchorBooks, New York.Google Scholar
  16. Heinsohn, R. and Packer, C. (1995), Complex cooperative strategies in groupterritorial african lions, Science 269(1), 1260–1262.Google Scholar
  17. Hirshleifer, J. and Martinez Coll, J.C. (1988), What strategies can support the evolutionary emergence of cooperation, Journal of Conflict Resolution, 32(2), 367–398.Google Scholar
  18. Hoffman, R. (2000), Twenty years on: The evolution of cooperation revisited, Journal of Artificial Societies and Social Simulation, (On-Line), 3(2). Available: Scholar
  19. Holland, J.H. (1975), Adaption in Natural and Artificial Systems, University of Michigan Press: Ann Arbor, MI.Google Scholar
  20. Johnson, N.L. and Kotz, S. (1969), Distributions in Statistics, Houghton Mifflin: Boston, MA.Google Scholar
  21. Latane, B. (1981), The psychology of social impact, American Psychologist, 36, 343–365.Google Scholar
  22. Lomborg, B. (1992), Game theory vs. multiple agents: the iterated prisoner's dilemma, In Castelfranchi, C., and Werner, E. (eds.), Artificial Social Systems, Springer-Verlag, pp.69–93.Google Scholar
  23. Macy, M.W. and Flache, A. (2002), Learning dynamics in social dilemmas. Proceedings of the National Academy of Sciences U.S.A. May 14; 99(10): 7229–36.Google Scholar
  24. Marinoff, L. (1992), Maximizing expected utilities in Prisoner's dilemma, Journal of Conflict Resolution 36, 183–216.Google Scholar
  25. Marshall, G.C. (1945), Biennial report of the chief of staff of the US army, The United States News, October 10, 1945.Google Scholar
  26. Milinski, M., (1987), Tit fortat in sticklebacks and the evolution of cooperation, Nature 325(29) 433–435.Google Scholar
  27. Nowak, M. and Sigmund, K. (1993), A strategy of win-stay, lose-shift that outperforms tit-for-tat in the prisoner's dilemma game, Nature 364, 56–58.CrossRefGoogle Scholar
  28. Roberts, G. and Sherratt, T.N. (1998), Development of cooperative relationships through increasing investment, Nature 394, 175–179.Google Scholar
  29. Sigmund, K. (1993), Games of Life, Oxford University Press, Oxford.Google Scholar
  30. Shubik, M. (1970), Game theory, behavior, and the paradox of the prisoner's dilemma: three solutions, Journal of Conflict Resolution, 14, 181–193.Google Scholar
  31. Suleiman, R. and Fischer, I. (1996), The Evolution of cooperation in a simulated intergroup conflict, in W.B.G. Liebrand, and D.M. Messick (eds.), Frontiers in Social Dilemma Research, Springer, Berlin, pp. 419–438.Google Scholar
  32. Suleiman, R. and Fischer, I. (2000), When one decides for many: The effect of delegation methods on cooperation in simulated inter-group conflicts, Journal of Artificial Societies and Social Simulation, (On-Line), 3 (4). Available: Scholar
  33. Wilson, D.S. and Dugatkin, L.A. (1997), Group selection and assorative interactions, The American Naturalist, 149(2), 336–351.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Ilan Fischer
    • 1
  1. 1.Department of Behavioral SciencesBen-Gurion University of the NegevIsrael. E-mail

Personalised recommendations