Cooperation prevails when individuals adjust their social ties

F.C. Santos, J.M. Pacheco, and T. Lenaerts
PLoS Computational Biology 2(10), e140, 2006.


Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.


In social networks, some individuals interact with more people and more often than others. In this context, one may wonder: under which conditions are social beings willing to be cooperative? Current models proposed in the context of evolutionary game theory cannot explain cooperation in communities with a high average number of social ties. Santos, Pacheco, and Lenaerts show that when individuals are able to simultaneously alter their behaviour and their social ties, cooperation may prevail. Moreover, the structure of the final networks corresponds to those found in empirical data. Their article concludes that the more individuals interact, the more they must be able to promptly adjust their partnerships for cooperation to thrive. Consequently, to understand the occurrence of cooperative behaviour in realistic settings, both the evolution of the complex network of interactions and the evolution of strategies should be taken into account simultaneously.

This paper in PLoS Comp Biol

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