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Evolution of Cooperative Networks and the Emergence of Leadership


  • M.G. Zimmermann, V. M. Eguiluz


A generic property of biological, social and economical networks is their ability to evolve in time, creating or supressing links. We model this situation with an adaptive network of agents playing a Prisoner's Dilemma game. Each agent plays with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. Furthermore we allow the agents adapt their local neighborhood according to their satisfaction level and the strategy played. Therefore each agent will have diverse environments that induces an interesting dynamics in the cooperation fraction of the whole network. In the absence of noise, a steady state is always reached, where the strategies and the neighborhoods remain stationary, and where for a wide range of parameter values, an almost full cooperative outcome is obtained. The topology of the network in these states reveals that cooperators with a large number of connections emerges. These "leaders" are shown to be very important in understanding the global stability of the final steady state. If the "leaders" are perturbated, then global cascades arise and the system oscillates between the nearly full defection network and the fully cooperative outcome, before settling again in a nearly fully cooperative outcome.

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  • M.G. Zimmermann, V. M. Eguiluz, 2001. "Evolution of Cooperative Networks and the Emergence of Leadership," Computing in Economics and Finance 2001 171, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:171

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    References listed on IDEAS

    1. Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.
    2. Dan Ashlock & Mark D. Smucker & E. Ann Stanley & Leigh Tesfatsion, 1995. "Preferential Partner Selection in an Evolutionary Study of Prisoner's Dilemma," Game Theory and Information 9501002, EconWPA, revised 20 Jan 1995.
    3. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. Michael D. Cohen & Rick L. Riolo & Robert Axelrod, 1999. "The Emergence of Social Organization in the Prisoner's Dilemma: How Context-Preservation and Other Factors Promote Cooperation," Working Papers 99-01-002, Santa Fe Institute.
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    7. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 137-156.
    8. Young, H.P., 1999. "Diffusion in Social Networks," Papers 2, Brookings Institution - Working Papers.
    9. Kirchkamp, Oliver, 2000. "Spatial evolution of automata in the prisoners' dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 239-262, October.
    10. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    11. Hirshlifer, David & Rassmusen, Eric, 1989. "Cooperation in a repeated prisoners' dilemma with ostracism," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 87-106, August.
    12. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
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    Cooperation -- Evolutionary Game Theory -- Stochastic Networks -- Prisoner Dilemma;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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