Group diversity promotes cooperation in the spatial public goods game

In this letter, the group diversity which reflects the inhomogeneity of social communities is introduced into the spatial public goods game. The diversity is realized by rescaling the multiplication factor r to follow three distributions: uniform distribution, exponential distribution and power-law distribution. During the evolution, each individual selects one of its neighbors randomly, and then updates its strategy depending on the difference of their payoffs. We investigate how the cooperation is affected by the inhomogeneity of r at the noise level κ=0.1, and find that cooperation can be remarkably promoted for each distribution. Particularly, the uniform distribution enables the best cooperation level, while the power-law distribution induces the lowest cooperation level for most of the range of the parameters. Besides, it is shown that there exists an optimal value of A (the amplitude of the undulation of the three distributions) resulting in the highest cooperation for the exponential and power-law distributed cases. Moreover, the effect of noise on the cooperation is studied. It is represented that compared with the original version, the emergence of cooperation is remarkably promoted over a large range of noise level, and cooperation in the case of power-law distribution is most immune to the noise. Meanwhile, we also prove that the variation of cooperator density with κ is closely dependent on the type of distribution of the multiplication factor r and its average value over all the groups