A homoclinic route to asymptotic full cooperation in adaptive networks and its failure
Gerd Zschaler, Arne Traulsen and Thilo Gross
New J. Phys. 12, 093015, 2010
We consider the evolutionary dynamics of a cooperative game on an adaptive network, where the strategies of agents (cooperation or defection) feed back on their local interaction topology. While mutual cooperation is the social optimum, unilateral defection yields a higher payoff and undermines the evolution of cooperation. Although no a priori advantage is given to cooperators, an intrinsic dynamical mechanism can lead asymptotically to a state of full cooperation. In finite systems, this state is characterized by long periods of strong cooperation interrupted by sudden episodes of predominant defection, suggesting a possible mechanism for the systemic failure of cooperation in real-world systems.
Figure 1: Time series of the fraction of cooperators in an adaptive network for different rewiring rates \(p\). When rewiring occurs almost at random (\(\alpha = 0.1\), red), cooperation and defection coexist at a stationary level for all \(p\). When players following the more successful strategy keep the link with high probability (\(\alpha = 30\), black), oscillations appear as the rate of rewiring exceeds a critical threshold.