On the Structural Robustness of Evolutionary Models of Cooperation

  • Segismundo S. Izquierdo
  • Luis R. Izquierdo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4224)


This paper studies the structural robustness of evolutionary models of cooperation, i.e. their sensitivity to small structural changes. To do this, we focus on the Prisoner’s Dilemma game and on the set of stochastic strategies that are conditioned on the last action of the player’s opponent. Strategies such as Tit-For-Tat (TFT) and Always-Defect (ALLD) are particular and classical cases within this framework; here we study their potential appearance and their evolutionary robustness, as well as the impact of small changes in the model parameters on their evolutionary dynamics. Our results show that the type of strategies that are likely to emerge and be sustained in evolutionary contexts is strongly dependent on assumptions that traditionally have been thought to be unimportant or secondary (number of players, mutation-rate, population structure...). We find that ALLD-like strategies tend to be the most successful in most environments, and we also discuss the conditions that favor the appearance of TFTlike strategies and cooperation.


Evolution of Cooperation Evolutionary Game Theory Iterated Prisoner’s Dilemma Tit for Tat Agent-based Modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Axelrod, R.: The Evolution of Cooperation. Basic Books USA (1984)Google Scholar
  2. Bendor, J., Swistak, P.: Types of evolutionary stability and the problem of cooperation. Proceedings of the National Academy of Sciences USA 92, 3596–3600 (1995)zbMATHCrossRefGoogle Scholar
  3. Bendor, J., Swistak, P.: Evolutionary Equilibria: Characterization Theorems and Their Implications. Theory and Decision 45, 99–159 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  4. Gotts, N.M., Polhill, J.G., Law, A.N.R.: Agent-based simulation in the study of social dilemmas. Artificial Intelligence Review 19(1), 3–92 (2003)CrossRefGoogle Scholar
  5. Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  6. Beggs, A.: Stochastic evolution with slow learning. Economic Theory 19, 379–405 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. Imhof, L.A., Fudenberg, D., Nowak, M.A.: Evolutionary cycles of cooperation and defection. Proceedings of the National Academy of Sciences USA 102(31), 10797–10800 (2005)CrossRefGoogle Scholar
  8. Nowak, M.A., Sasaki, A., Taylor, C., Fudenberg, D.: Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)CrossRefGoogle Scholar
  9. Taylor, C., Fudenberg, D., Sasaki, A., Nowak, M.A.: Evolutionary Game Dynamics in Finite Populations. Bulletin of Mathematical Biology 66, 1621–1644 (2004)CrossRefMathSciNetGoogle Scholar
  10. Nowak, M.A., Sigmund, K.: The evolution of stochastic strategies in the Prisoners Dilemma. Acta Applicandae Mathematicae 20, 247–265 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  11. Nowak, M.A., Sigmund, K.: Tit for tat in heterogeneous populations. Nature 355, 250–253 (1992)CrossRefGoogle Scholar
  12. Nowak, M.A., Sigmund, K.: Invasion Dynamics of the Finitely Repeated Prisoner’s Dilemma. Games and Economic Behavior 11(2), 364–390 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 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 Kaufman, San Francisco (1987); Reprinted in Axelrod, R.: The complexity of cooperation. Agent-based models of competition and collaboration. Princeton University Press, Princeton (1997)Google Scholar
  14. Binmore, K.: Playing Fair: Game Theory and the Social Contract I. MIT Press, Cambridge (1994)Google Scholar
  15. Binmore, K.: Review of the book: The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. In: Axelrod, R. (ed.), Princeton University Press, Princeton (1997); Journal of Artificial Societies and Social Simulation 1(1) (1998),
  16. Probst, D.: On Evolution and Learning in Games. PhD thesis, University of Bonn (1996)Google Scholar
  17. Linster, B.: Evolutionary stability in the repeated Prisoners’ Dilemma played by two-state Moore machines. Southern Economic Journal 58, 880–903 (1992)CrossRefGoogle Scholar
  18. Wilensky, U.: NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL (1999),
  19. Kulkarni, V.G.: Modelling and Analysis of Stochastic Systems. Chapman & Hall/CRC (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Segismundo S. Izquierdo
    • 1
  • Luis R. Izquierdo
    • 2
  1. 1.Social Systems Engineering Centre (INSISOC)University of ValladolidSpain
  2. 2.The Macaulay Institute, CraigiebucklerAberdeenUK

Personalised recommendations