Table 1.
Payoff matrix of the Prisoner's Dilemma.
Table 2.
Statistical properties of e-mail and PGP networks.
Figure 1.
Evolution of cooperation in real social networks.
Black lines: Density of cooperators as a function of b, obtained by numerical simulations on the email (left) and PGP (right) networks. Red lines: Density of cooperators on random networks generated from the original ones by a rewiring procedure that preserves the degree distribution(see text). The equilibrium densities of cooperators have been obtained by averaging 500 generations, after a transient time of 750 generation steps. Each point corresponds to an average over 1000 independent simulations with 50% cooperators and defectors as the initial condition.
Figure 2.
Community structures of the email and PGP networks.
Top: Community structures of the email (A) and PGP (B) networks. Nodes correspond to communities (where size is proportional to their number of members) and links represent cross-connections (where width corresponds to the number of inter-connetions). Bottom: Typical examples of the communities detected in the email (C) and PGP (D) networks. Solid links join nodes of the community, dashed links join this community with others.
Table 3.
Statistical properties of synthetic networks with 10000 nodes and 75 communities.
Figure 3.
Evolution of cooperation in four synthetic networks.
Cases A and D correspond, respectively, to the synthetic classes of networks akin to the email and PGP real networks. In case A communities have been built as Erdos-Renyi random graphs (pintra = 1.5×10−1), and the probability of interconnection between communities (pinter) is 5×10−2. Communities in case D are constructed as independent scale-free networks (Barabasi-Albert with k0 = 3), and after they have been sparsely interconnected with (pinter = 1.5×10−5). Case B has been obtained from D by increasing the probability pinter to 3.5×10−4, and case C corresponds to A reducing this probability to 7.5×10−4. Simulations have been performed as indicated in Fig. 1.