Cooperation in an Adaptive Network

We study the dynamics of a set of agents distributed in the
nodes of an adaptive network. Each agent plays with all its neighbors
a weak prisoner´s dilemma collecting a total pay-off. We study
the case where the network adapts locally depending on the total
pay-off of the agents. In the parameter regime considered, a steady
state is always reached (strategies and network remain stationary),
where cooperation is highly enhanced. However, when the adaptability
of the network and the incentive for defection are high enough,
we show that a slight perturbation of the steady state induces
large oscillations (with cascades) in behavior between the nearly
all-defectors sate and the all-cooperators outcome.