We study the same social dilemmas of cooperation as in .

(Top left panel) Cumulative degree distributions (see ) for the most difficult challenge to cooperation in our parameter space: the PD with *T =* 2 and *S = −*1, corresponding to *b/c =* 2. Starting from a distribution exhibiting a sharp cutoff at *k*_{max} = z, as soon as *W >* 0 the distribution widens, resulting in both single-scale networks (*W* = 0.5) and broad-scale networks (*W* > 3), reflecting the increase in the overall heterogeneity of the pattern of ties in the population.

(Contour plots) The amount of heterogeneity, measured in terms of the variance of the degree distribution (see ), depends on the underlying social dilemma and the value *W*. In other words, different challenges to cooperation lead to the evolution of different societal organization, in which simple-to-broad–scale heterogeneity develops as soon as *W ≠* 0*.* The red color corresponds to the area of the game where the conflict between strategy and topology dynamics is the strongest. For small *W,* heterogeneity is maximal for the SG and large *T*. For *W =* 4, heterogeneity is maximal for the PD with (*T =* 2, *S =* −1), in spite of the fact that cooperators wipe out defectors for all dilemmas.

## PubMed Commons