Abstract
A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner’s Dilemma game, where each agent plays with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. We allow the agents to adapt their local neighborhood according to their satisfaction level and the strategy played. We show that a steady state is reached, where the strategy and network configurations remain stationary. While the fraction of cooperative agents is high in these states, their average payoff is lower than the one attained by the defectors. The system self-organizes in such a way that the structure of links in the network is quite inhomogeneous, revealing the occurrence of cooperator “leaders” with a very high connectivity, which guarantee that global cooperation can be sustained in the whole network. Perturbing the leaders produces drastic changes of the network, leading toglobal dynamical cascades.These cascades induce a transient oscillation in the population of agents between the nearly all-defectors state and the all-cooperators outcome, before setting again in a state of high global cooperation.
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References
D. Ashlock, M. D. Smucker, and L. Tesfatsion. Preferential partner selection in an evolutionary study of Prisoner’s Dilemma.BioSystems37(1–2):99–125, 1996.
R. AxelrodThe Evolution of Cooperation.Basic Books, New York, 1984.
R. Axelrod and W. D. Hamilton. The evolution of cooperation.Science211:1390–1396, 1981.
M. Cohen, R. Riolo, and R. Axelrod. The emergence of social organization in the prisoner’s dilemma: how context-preservation and other factors promote cooperation. Santa Fe Institute Working Paper 99–01–002, 1999.
S. Goyal and S. Joshi. Networks of collaboration in oligopoly. Mimeo, 1999.
B. A. Huberman and N. S. Glance. Evolutionary games and computer simulations.Proc. Natl. Acad. Sci. USA90:7716–7718, 1993.
M. O. Jackson and A. Watts. The evolution of social and economic networks. Vanderbilt University, Mimeo, 1999.
O. Kirchkamp. Spatial evolution of automata in the prisoners’ dilemma. Discussion Paper B-330, Rheinische Friedrich Wilhelms Universität Bonn, Mimeo, 1995.
A. Kirman. Aggregate activity and economic organisation.Revue Economique des sciences sociales113:189–230, 1999.
K. Lindgren. Evolutionary dynamics in game-theoretic models. In Durlauf, Arthur and Lane, editorsThe Economy as an Evolving Complex System IIvolume XXVII, pages 337–367. SFI Studies in the Sciences of Complexity, 1997.
K. Lindgren and M. G. Nordahl. Evolutionary dynamics of spatial games.Physica D75:292–309, 1994.
A. Mukherji, V. Rajan, and J. R. Slagle. Robustness of cooperation.Nature379:125–126, 1996.
M. A. Nowak, S. Bonhoeffer, and R. M. May. Spatial games and the maintenance of cooperation.Proc. Natl. Acad. Sci. USA91:4877–4881, 1994.
M. A. Nowak and R. M. May. Evolutionary games and spatial chaos.Nature359:826–829, 1992.
M. A. Nowak and R. M. May. The spatial dilemmas of evolution.Int. Jour. of Bif. and Chaos3(1):35–78, 1993.
A. Watts. A dynamic model of network formation. Vanderbilt University, Mimeo, 1999.
D. J. Watts and S. H. Strogatz. Collective dynamics of small-world networks.Nature393:440–442, 1998.
J. Weibull. Evolutionary Game Theory.MIT University Press, 1996.
M. G. Zimmermann, V. M. Eguluz, M. San Miguel, and A. Spadaro. Cooperation in an Adaptive Network. In Ballot and Weisbuch, editorsApplications of Simulation to Social SciencesHermes Science Publications (Paris, France), 2000.
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Zimmermann, M.G., Eguíluz, V.M., Miguel, M.S. (2001). Cooperation, Adaptation and the Emergence of Leadership. In: Kirman, A., Zimmermann, JB. (eds) Economics with Heterogeneous Interacting Agents. Lecture Notes in Economics and Mathematical Systems, vol 503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56472-7_6
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DOI: https://doi.org/10.1007/978-3-642-56472-7_6
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