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Cooperation, adaptation and the emergence of leadership

Zimmermann, Martin; Eguíluz, Victor M.; San Miguel, Maxi
Proc. of Workshop on Economics with Heterogeneous Interacting Agents. Eds.J. B. Zimmerman and A. Kirman , Springer Verlag 73-86 (2001)

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 to global 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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