Extended Data Fig. 2: Evolution of producers can be possible for ff-goods but not for pp-goods.

a, PC updating on Erdös-Rényi graphs of size N = 100 for various edge-inclusion probabilities, p. If p is sufficiently small, the critical benefit-to-cost ratio is positive for both pp- and ff-goods, but for slightly larger p values this ratio can be positive for ff-goods and negative for pp-goods. In the latter case, producers cannot evolve under any b/c ratio for pp-goods, but they can evolve for ff-goods as long as b/c is sufficiently large. b, PC updating on small-world networks with different rewiring probabilities, p. Again, there are many examples for which the critical benefit-to-cost ratio is positive for ff-goods but negative for pp-goods.