A simple rule for the evolution of cooperation on graphs and social networks

Abstract

The evolution and maintenance of cooperative behaviour take some explaining. Cooperative groups can be undermined by ‘cheaters’ who selfishly exploit common resources, and a large body of theory predicts that cheats will usually displace cooperators. But a possible explanation of why cheats don't always prosper emerges from competition experiments between strains of yeast that act as cooperators and cheaters, competing for glucose and utilizing it either efficiently or ‘selfishly’. The results show that both strategies can coexist, because both are associated with costs and benefits. There is a cost to cheating; in this instance the production of fewer offspring than the opposition. A graphic — really — demonstration that natural selection can favour cooperation comes in a study by Ohtsuki et al. of the evolutionary dynamics of structured ‘virtual’ populations formed of points on a graph. Cooperation is favoured if the benefit of the altruistic act divided by the cost exceeds the average number of neighbours. So cooperation can evolve as a consequence of this ‘social viscosity’ even in the absence of reputation effects or strategic complexity. Natural selection generally favours cooperation if the benefit of the altruistic act divided by the cost exceeds the average number of neighbours, indicating that cooperation can evolve as a consequence of ‘social viscosity’, even in the absence of reputation effects or strategic complexity. A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals1,2,3,4. Human society is based to a large extent on mechanisms that promote cooperation5,6,7. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs8,9,10,11,12,13,14,15,16,17. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks18,19,20,21,22,23,24. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks25,26: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of ‘social viscosity’ even in the absence of reputation effects or strategic complexity.