Evolution of cooperation in networks: well-connected cooperators can enhance cooperation but are counteracted by Trojan horses.
Cooperative behaviour is widespread in nature, but explaining how cooperation evolves constitutes a major scientific challenge. Simulation models has shown that social network structure plays a key role in rendering cooperation evolutionarily stable. However, not much is known about the importance of initial conditions for the evolution of cooperation in networks. Knowledge about this is essential for judging to which extent results from modelling and experiments can tell us something about the real world. Here, we investigate how cooperation is affected by the initial network positions of cooperators in different networks, by means of game-theory based simulation models. We find that placing cooperators on high-degree nodes enhances cooperation in standard scale-free networks but not in standard Poisson networks. In contrast, under increased degree assortativity, Poisson networks can maintain high levels of cooperation, even exceeding those of scale-free networks, when the initial placement of cooperators is perfectly correlated to node degree. When the correlation is not perfect however, defectors placed within clusters of cooperators can act as Trojan horses, allowing defection to invade. The results are relevant both to computer simulations of cooperation in networks and in particular to real-world cooperation experiments, where the number of replications is typically low and stochastic initial correlations between cooperativeness and network position may be present.