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On the Structural Robustness of Evolutionary Models of Cooperation

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Intelligent Data Engineering and Automated Learning – IDEAL 2006 (IDEAL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4224))

Abstract

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.

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References

  • Axelrod, R.: The Evolution of Cooperation. Basic Books USA (1984)

    Google Scholar 

  • 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)

    Article  MATH  Google Scholar 

  • Bendor, J., Swistak, P.: Evolutionary Equilibria: Characterization Theorems and Their Implications. Theory and Decision 45, 99–159 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  • Beggs, A.: Stochastic evolution with slow learning. Economic Theory 19, 379–405 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Nowak, M.A., Sasaki, A., Taylor, C., Fudenberg, D.: Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 646–650 (2004)

    Article  Google Scholar 

  • Taylor, C., Fudenberg, D., Sasaki, A., Nowak, M.A.: Evolutionary Game Dynamics in Finite Populations. Bulletin of Mathematical Biology 66, 1621–1644 (2004)

    Article  MathSciNet  Google Scholar 

  • Nowak, M.A., Sigmund, K.: The evolution of stochastic strategies in the Prisoners Dilemma. Acta Applicandae Mathematicae 20, 247–265 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Nowak, M.A., Sigmund, K.: Tit for tat in heterogeneous populations. Nature 355, 250–253 (1992)

    Article  Google Scholar 

  • Nowak, M.A., Sigmund, K.: Invasion Dynamics of the Finitely Repeated Prisoner’s Dilemma. Games and Economic Behavior 11(2), 364–390 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • 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 

  • Binmore, K.: Playing Fair: Game Theory and the Social Contract I. MIT Press, Cambridge (1994)

    Google Scholar 

  • 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), http://jasss.soc.surrey.ac.uk/1/1/review1.html

  • Probst, D.: On Evolution and Learning in Games. PhD thesis, University of Bonn (1996)

    Google Scholar 

  • Linster, B.: Evolutionary stability in the repeated Prisoners’ Dilemma played by two-state Moore machines. Southern Economic Journal 58, 880–903 (1992)

    Article  Google Scholar 

  • Wilensky, U.: NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL (1999), http://ccl.northwestern.edu/netlogo/

  • Kulkarni, V.G.: Modelling and Analysis of Stochastic Systems. Chapman & Hall/CRC (1995)

    Google Scholar 

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Izquierdo, S.S., Izquierdo, L.R. (2006). On the Structural Robustness of Evolutionary Models of Cooperation. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2006. IDEAL 2006. Lecture Notes in Computer Science, vol 4224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875581_21

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  • DOI: https://doi.org/10.1007/11875581_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45485-4

  • Online ISBN: 978-3-540-45487-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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